For the graph below, match the question and correct calculation from the list below. This is the force profile in the x-direction for a baseball bat on a 95.0 g ball initially at rest (tee ball). Prompts (1) The impulse on the ball in the first 50 ms. (2) The velocity of the ball at the end of the first 50 ms. (3) The change in momentum for the ball from 50 ms to 100 ms. (4) The speed of the ball after 100 ms. Answers Select match Select match Select match
A ball weighing 25.4 N is tied to a string fixed to the ceiling. The string makes a 33.2∘ angle with the ceiling. Initially, the ball is held in place by a force F→ that is perpendicular to the string. θ1 = 33.2∘ What is the radial acceleration of the ball immediately after the force F is removed? m/s2
Four forces act on an object, given by A = 37.3 N east, B = 43.3 N north, C = 82.7 N west, and D = 94.7 N south. (Assume east and north are directed along the +x-axis and +y-axis, respectively.) (a) What is the magnitude of the net force (in N ) on the object? N (b) What is the direction of the force? (Enter your answer in degrees counterclockwise from the +x-axis.) - counterclockwise from the +x-axis
A block of mass m1 = 16.0 kg is connected to a block of mass m2 = 32.0 kg by a massless string that passes over a light, frictionless pulley. The 32.0−kg block is connected to a spring that has negligible mass and a force constant of k = 300 N/m as shown in the figure below. The spring is unstretched when the system is as shown in the figure, and the incline is frictionless. The 16.0−kg block is pulled a distance h = 18.0 cm down the incline of angle θ = 40.0∘ and released from rest. Find the speed of each block when the spring is again unstretched. vm1 = m/s vm2 = m/s
The figure here shows a plot of potential energy U versus position x of a 0.852 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are UA = 15.0 J, UB = 35.0 J and UC = 45.0 J. The particle is released at x = 4.50 m with an initial speed of 7.89 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x = 4.00 m ? Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.50 m at speed 7.89 m/s. (d) If the particle can reach x = 7.00 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x = 5.00 m?
A 6 Kg block has an initial velocity 5 m/s up a 30 degree incline. When the block has moved 1.25 m up the incline it has a the velocity, 2.8 m/s up the incline. There is friction. Calculate the magnitude of the work done by friction acting on the block as the block moves 1.25 m up the incline.
A plane, diving with constant speed at an angle of 42.6∘ with the vertical, releases a projectile at an altitude of 696 m. The projectile hits the ground 5.26 s after release. (a) What is the speed of the plane? (b) How far does the projectile travel horizontally during its flight? What were the magnitudes of the (c) horizontal and (d) vertical components of its velocity just before striking the ground? (State your answers to (c) and (d) as positive numbers.) (a) Number Units (b) Number Units (c) Number Units (d) Number Units
Two test charges are located in the xy plane. Charge q1 = −4.250 nC and is located at x1 = 0.00 m, y1 = 0.6800 m. Charge q2 = 3.200 nC and is located at x2 = 1.500 m, y2 = 0.400 m. Calculate the x and y components, Ex and Ey, respectively, of the electric field E→ at the origin, (0, 0). The Coulomb force constant is 1/(4πϵ0) = 8.99×109 N⋅m2 /C2. Ex = N/C Ey = N/C
A horizontal spring (with spring constant 180 N/m) is attached to the wall at the left, and a 15 Kg block on the right at rest. There is no friction. A 10 Kg block has a speed 8 m/s approaching the 15 Kg block. The 10 Kg block collides with the 15 Kg block and the blocks stick together. After the collision, the two blocks remain stuck together and oscillate back and forth as simple harmonic motion. Calculate the maximum compression of the spring. 1.2 m 1.4 m 1.8 m 3.2 m 3.0 m
A block of mass m = 5.78 kg is attached to a spring that is resting on a horizontal, frictionless table. The block is pushed into the spring, compressing it by 5.00 m, and is then released from rest. The spring begins to push the block back toward the equilibrium position at x = 0 m. The graph shows the component of the force (in newtons) exerted by the spring on the block versus the position of the block (in meters) relative to equilibrium. Use the graph to answer the questions. How much work W is done by the spring in pushing the block from its initial position at x = −5.00 m to x = 2.86 m? W = J What is the speed v of the block when it reaches x = 2.86 m? v = m/s What is the maximum speed vmax of the block? vmax = m/s
A box slides from rest down a frictionless ramp inclined at 32.0∘ with respect to the horizontal and is stopped at the bottom of the ramp by a spring with a spring constant of k = 3.00×104 N/m. If the box has a mass of 12.0 kg and slides 3.00 m from the point of release to the point where it comes to rest against the spring, determine the compression (in m) of the spring when the box comes to rest. m
You have a light spring which obeys Hooke's law. This spring stretches 2.52 cm vertically when a 2.10 kg object is suspended from it. Determine the following. (a) the force constant of the spring (in N/m) N/m (b) the distance (in cm ) the spring stretches if you replace the 2.10 kg object with a 1.05 kg object cm (c) the amount of work (in J) an external agent must do to stretch the spring 8.70 cm from its unstretched position J
An arrow (m = 5.0 g) is fired at a styrofoam block (m = 150 g) sitting on the edge of a frictionless table. The tabletop is 1.1 m above ground. The arrow enters the block horizontally at val = 35 m/s and passes through to the other side, exiting horizontally at va2 = 15 m/s. ( 6 marks) a) Determine the speed of the styrofoam after the arrow exits the block. (2 marks) b) Determine where the Styrofoam will land with respect to the arrow. Assume the arrow passed right through the centre of mass of the block, and both objects drop the same vertical distance to the ground. (4 marks)
Blocks A, B, and C are attached to two strings that pass over frictionless pulleys as shown in the figure. The masses are: mA = 16 Kg mB = 24 Kg mC = 8 Kg The pulleys are frictionless and massless. There is no friction between block B and the table. The blocks are released from rest. After being release from rest, the objects move. When the blocks have moved 1 meter, calculate the speed of the blocks. Answer in meters per second. Numeric entry only.
Suppose the skateboarder shown in the drawing reaches a height of 2.40 m above the right side of the semicircular ramp. He then makes an incomplete midair turn and ends up sliding down theright side of the ramp on his back. When the skateboarder reaches the bottom of the ramp, his speed is 7.00 m/s. The skateboarder's mass is 68.0 kg, and the radius of the semicircular ramp is 2.40 m. What is the average frictional force exerted on the skateboarder by the ramp?
A vertical spring with force constant 180 N/m is compressed by an attached 15 Kg block at rest. A separate 10 Kg block glued to the 15 Kg block, and the combined 25 Kg mass is given a downward push of 4 meters per second. This push happens at the original location of the 15 Kg block. Calculate the distance (in meters) the mass goes down from the initial release to the lowest turn around point. Enter number only.
Disturbed by speeding cars outside his workplace, Nobel laureate Arthur Holly Compton designed a speed bump (called the "Holly hump") and had it installed. Suppose a 1800−kg car passes over a hump in a roadway that follows the arc of a circle of radius 19.0 m as in the figure below. (i) (a) If the car travels at 26.4 km/h what force does the road exert on the car as the car passes the highest point of the hump? magnitude N direction (b) What is the maximum speed the car can have without losing contact with the road as it passes this highest point? km/h
An accelerometer-a device to measure acceleration-can be as simple as a small pendulum hanging in an airplane cockpit. An essentially similar accelerometer is found in the inner ear of vertebrates. Suppose you are flying a small plane in a straight, horizontal line and your accelerometer hangs at a constant angle of P = 28.0∘ behind the vertical, as shown in the figure. What is your acceleration? Enter a positive answer if the acceleration is in the direction of motion and enter a negative answer if the acceleration is opposite to the direction of motion. Where P = 28.0∘ m/s2
Objects of masses m1 = 4.0 kg and m2 = 9.0 kg are connected by a light string that passes over a frictionless pulley in the figure. The object m1 is held at rest on the floor, and m2 rests on a fixed incline of θ = 40.5∘. The objects are released from rest, and m2 slides 1.3 m down the slope of the incline in 3.95 s. (THIS IS AN EXAM QUESTION.) 18.) Find the magnitude of the acceleration of m1 (in m/s2). (A) 2.0 (B) 4.0 (D) 0.17 (E) 0.13 (C) 9.8 19.) Find the coefficient of kinetic friction between m2 and the incline. (A) 0.58 (B) 0.30 (C) 0.24 (D) 0.085 (E) 1.64
The figure below shows a spring with a force constant 300 [Nm−1] compressed by a 2.5[kg] block held at rest initially. The compression is 18.0 [cm]. The block is then released and slides freely across a smooth surface until it reaches a rough patch 10 [cm] long with μ = 0.72 Figure 2: Mass on spring. a - Find the speed of the block before it reaches the rough patch. b - Find the speed of the block after crossing the rough patch.
A person pushes a 11.9-kg shopping cart at a constant velocity for a distance of 28.6 m on a flat horizontal surface. She pushes in a direction 26.4∘ below the horizontal. A 44.0-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force. (a) Number Units
Ron and Lilly are in a carnival ride that is swinging them outwards in a horizontal circular motion. Choose the correct Free Body Diagram of the forces acting on Ron at the instant shown. a) b) c) d) e) (d) (b) (a) (c) (e0
Consider the charge pair, −q and- q, below. They have a charge of −50.0 μC. Point P is a point in space. The distance r is equal to 20.0 cm. Determine the total voltage at point P due to the charges.
Assuming the sled moves up the ramp with constant speed. Which force does the most work in magnitude (ignoring the sign of the work)? A. Tension force B. Gravity C. Normal Force D. Tension force and gravity do the work of the same magnitude E. Normal force and gravity do the work of the same magnitude
A ramp of mass M is at rest on a horizontal surface. A small cart of mass m is placed at the top of the ramp and released. What are the velocities of the ramp and the cart relative to the ground at the instant the cart leaves the ramp? (Assume the positive direction is to the right. Indicate the direction with the signs of your answers. Use the following as necessary: M, m, g, and h. vcart = vramp =
The skateboarder in the drawing starts down the left side of the ramp with an initial speed of 5.4 m/s. Neglect nonconservative forces, such as friction and air resistance, and find the height h of the highest point reached by the skateboarder on the right side of the ramp.
A skier slides down a frictionless slope of length r = 1.67 km which makes an angle with the horizontal of θ = 27.7∘. At the bottom of the slope she encounters a horizontal rough patch. If she then glides through the rough patch for a distance x = 3.33 km before stopping, what was the average coefficient of kinetic friction between her skis and the surface of the rough patch?
A box has a weight of 160 N and is being pulled across a horizontal floor by a force that has a magnitude of 100 N. The pulling force can point horizontally, or it can point above the horizontal at an angle θ. When the pulling force points horizontally, the kinetic frictional force acting on the box is twice as large as when the pulling force points at the angle θ. Find θ. Number Units
A projectile is shot upward from the surface of Earth with an initial velocity of 137 meters per second. Use the position function below for free-falling objects. What is its velocity (in m/s ) after 2 seconds? After 12 seconds? (Round your answers to one decimal place.) s(t) = −4.9t2 + v0t + s0 2 s m/s 12 s m/s
A projectile is fired from the platform at B. The shooter fires his gun from point A at an angle of 30∘. Determine the muzzle speed of the bullet if it hits the projectile at C. (Answer: vA = 28.0 m/s)
Starting with an initial speed of 6.00 m/s at a height of 0.321 m, 32.94−kg ball swings downward and strikes a 5.65−kg ball that is at rest, as the drawing shows. (a) Using the principle of conservation of mechanical energy, find the speed of the 2.94−kg ball just before impact. (b) Assuming that the collision is elastic, find the velocity (magnitude and direction) of the 2.94 kg ball just after the collision. (c) Assuming that the collision is elastic, find the velocity (magnitude and direction) of the 5.65−kg ball just after the collision. (d) How high does the 2.94−kg ball swing after the collision, ignoring air resistance? (e) How high does the 5.65−kg ball swing after the collision, ignoring air resistance?
A projectile of mass 0.885 kg is shot straight up with an initial speed of 25.3 m/s. (a) How high would it go if there were no air resistance? (b) If the projectile rises to a maximum height of only 8.46 m, determine the magnitude of the average force due to air resistance. (a) Number Units (b) Number Units
Noninertial frame projectile. A device shoots a small ball horizontally with speed 0.204 m/s from height h = 0.806 m above an elevator floor. The ball lands at distance d from the base of the device directly below the ejection point. The vertical acceleration of the elevator can be controlled. What is the elevator's acceleration magnitude a if d is (a) 14.0 cm, (b) 20.0 cm, and (c) 7.50 cm? (a) Number Units (b) Number Units (c) Number Units
An object of mass M is hanging by a light spring of force constant k from the ceiling, as shown in Fig. 3. A small ball of mass m which moves vertically upward collides with the object. After the collision, the object and the small ball stick together and oscillate in simple harmonic motion. Before the collision, the object is at rest. The speed of the small ball just before the collision is denoted as v. The acceleration of gravity is denoted as g. Answer the following questions. Fig. 3 (1) Find the amount of stretch of the spring from its natural length before the collision. (a) Mk (b) M/k (c) k/M (d) Mgk (e) Mg/k (f) k/Mg
The natural frequency of a spring-mass system is originally 1 rad/s. The spring-mass system is connected to an inverted pendulum, with the spring attached to the midpoint of the pendulum, which has a length of 2l. Determine the mass ratio r (r = M/m) that restricts the natural frequency of the assembled system to less or equal to 2 rad/s. (Neglect the gravity, sinθ ≈ θ, cosθ ≈ 1)
You attach one end of a spring with a force constant k = 813 N/m to a wall and the other end to a mass m = 2.62 kg and set the mass-spring system into oscillation on a horizontal frictionless surface as shown in the figure. To put the system into oscillation, you pull the block to a position xi = 7.36 cm from equilibrium and release it. (a) Determine the potential energy stored in the spring before the block is released. J (b) Determine the speed of the block as it passes through the equilibrium position. m/s (c) Determine the speed of the block when it is at a position xi/4. m/s
4.2 A block of mass m is connected by a string of negligible mass to a spring with spring constant K which is in turn fixed to a wall. The spring is horizontal and the string is hung over a pulley such that the mass hangs vertically. The pulley is a solid disk of mass M and radius R. As shown in the diagram below, the spring is initially in its equilibrium position and the system is not moving. a) Use energy methods, to determine the speed v of the block after it has fallen a distance h. Express your answer in terms of g, m, K, M and h. NOTE: Question 4.2 b) and c) on next page.
A copper rod of length 0.84 m is lying on a frictionless table (see the drawing). Each end of the rod is attached to a fixed wire by an unstretched spring that has a spring constant of k = 94 N/m. A magnetic field with a strength of 0.21 T is oriented perpendicular to the surface of the table. (a) What must be the direction of the current in the copper rod that causes the springs to stretch? (b) If the current is 13 A, by how much does each spring stretch? (a) Direction (b) Number Units
Block P of mass m is on a horizontal, frictionless surface and is attached to a spring with spring constant k. The block is oscillating with period TP and amplitude AP about the spring's equilibrium position x0. A second block Q of mass 2m is then dropped from rest and lands on block P at the instant it passes through the equilibrium position, as shown above. Block Q immediately sticks to the top of block P, and the two-block system oscillates with period TPQ and amplitude APQ. (a) Determine the numerical value of the ratio TPQ/TP.
The cart impacts the safety barrier with speed v0 = 4.00 m/s and is brought to a stop by the nest of nonlinear springs which provide a deceleration a = −k1x − k2x3, where x is the amount of spring deflection from the undeformed position and k1 and k2 are positive constants. If the maximum spring deflection is 490 mm and the velocity at half-maximum deflection is 3.56 m/s, determine the values for the constants k1 and k2. Answers: k1 = s−2 k2 = m−2s−2
The figure represents a sphere of mass m = 2.0⋅10−3 kg and charge q = 3.72⋅10−7 C, in equilibrium on an inclined plane of 25∘. The sphere is attached to a spring with spring constant k = 1.57 N/m and is immersed in a uniform horizontal electric field, of magnitude E = 7.2⋅104 N/C. The coefficient of static friction between the sphere and the plane is μs = 0.40. Determine the maximum elongation of the spring for the sphere to be in equilibrium.
A positively charged particle of mass 6.02×10−8 kg is traveling due east with a speed of 89.3 m/s and enters a 0.424-T uniform magnetic field. The particle moves through one-quarter of a circle in a time of 2.47×10−3 s, at which time it leaves the field heading due south. All during the motion the particle moves perpendicular to the magnetic field. (a) What is the magnitude of the magnetic force acting on the particle? (b) Determine the magnitude of its charge. (a) Number Units (b) Number Units
The mass m1 is supported by the 20 kg mass m2 and a 100 N horizontal force as shown. The static coefficient of friction between m1 and the ramp surface is 0.3 . Determine the range of mass, m1 for which this system will be in equilibrium. (20 pts)
A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water 5.00 m from the end of the slide in a time of 0.715 s after leaving the slide. Ignore friction and air resistance, find the height H in the drawing.
You want to get from a point A on the straight shore of the beach to a buoy which is 56 meters out in the water from a point B on the shore. B is 70 meters from you down the shore. If you can swim at a speed of 5 meters per second and run at a speed of 7 meters per second, at what point along the shore, x meters from B, should you stop running and start swimming if you want to reach the buoy in the least time possible? Find a formula for the time spent in terms of x T(x) = Find the value for x that will minimize the total time spent running and swimming. x =
A swimmer swims 1.1 mph in still water and wants to swim to a point B due north from her starting point directly across a river. If the current is 0.2 mph due east, at what angle θ should the swimmer swim to reach point B ? Round to the nearest tenth of a degree.
A swimmer, capable of swimming at a speed of 1.39 m/s in still water (i.e, the swimmer can swim with a speed of 1.39 m/s relative to the water), starts to swim directly across a 2.90-km-wide river. However, the current is 0.817 m/s, and it carries the swimmer downstream. (a) How long does it take the swimmer to cross the river? (b) How far downstream will the swimmer be upon reaching the other side of the river? (a) Number Units (b) Number Units
A swimmer, who is looking up from under the water (n = 1.333), sees a diving board directly above at an apparent height of 4.3 m above the water. What is the actual height of the diving board? Apparent position of diving board Diving board Number Units As an aid in understanding this problem, refer to Conceptual Example 4.
Suppose a block of mass m goes up an inclined plane plane with angle α. The initial velocity of the block is v0→. There is static (μs) and kinetic (μk) friction between the block and the plane. What is the maximum height that the block reaches if it starts with an initial velocity of v0 at the base of the inclined plane ( 2 pts )? After the block gets to its maximum height, what condition must be satisfied for it to descend back down the plane (2 pts)? Assuming the condition in (2) is met, with what velocity will it reach the base of the incline (2 pts)?
A swimmer crosses a river of width L by swimming with constant speed v. The river flows with a constant uniform speed u. At what angle θ should the swimmer swim to travel the least distance in crossing the river? Consider two cases: v ≥ u, and v < u.
A swimmer runs horizontally off a diving board with a speed of 3.32 m/s and hits the water a horizontal distance of 1.78 m from the end of the board. (a) Find the time it takes the swimmer to hit the water. (b) How high above the water was the diving board? (c) Just before the swimmer hits the water, what are his horizontal component of velocity and his vertical component of velocity? (d) What is the magnitude and direction of the swimmer's velocity just before he hits the water?
A force F→ is applied to a 1.5 -kg radio-controlled model car parallel to the x-axis as it moves along a straight track. The x-component of the force varies with the x-coordinate of the car as shown below. The model car is initially at rest at x = 0. Use the work-energy theorem to find the speed of the car at the following locations. (a) x = 2.0 m m/s (b) x = 3.0 m m/s (c) x = 4.0 m m/s
Work-Energy Theorem. Look at the Figure below; find the (a) Wnet (in J = joules), (b) KEf (in J = joules) of the package at he end of the push, using work and energy concepts. Initial velocity of the package is 0.455 m/s.
A dental X-ray typically affects 190 g of tissue and delivers about 4.1 μJ of energy using X-rays that have wavelengths of 0.025 nm. What is the energy Ephoton , in electron volts, of X-ray photons? Ephoton = How many photons, N, are absorbed during the dental X-ray? Assume the body absorbs all of the incident X-rays. N = photons
A student working in the physics laboratory connects a parallel-plate capacitor to a battery, so that the potential difference between the plates is 230 V. Assume a plate separation of d = 1.51 cm and a plate area of A = 25.0 cm2. When the battery is removed, the capacitor is plunged into a container of distilled water. Assume distilled water is an insulator with a dielectric constant of 80.0. (a) Calculate the charge on the plates (in pC) before and after the capacitor is submerged. (Enter the magnitudes.) before Qi = pC after Qf = pC (b) Determine the capacitance (in F) and potential difference (in V ) after immersion. Cf = F ΔVf = V (c) Determine the change in energy (in nJ ) of the capacitor. ΔU = nJ (d) What If? Repeat parts (a) through (c) of the problem in the case that the capacitor is immersed in distilled water while still connected to the 230 V potential difference. Calculate the charge on the plates (in pC) before and after the capacitor is submerged. (Enter the magnitudes. ) before Qi = pC after Qf = pC Determine the capacitance (in F) and potential difference (in V ) after immersion. Cf = F ΔVf = V Determine the change in energy (in nJ) of the capacitor. ΔU = nJ
As shown, the ]coefficient of kinetic friction between the surface and the larger block is 0.2, and the coefficient of kinetic friction between the surface and the smaller block is 0.29. If F = 15 N and M = 0.9 kg, what is the tension in the connecting string?
A water skier lets go of the tow rope upon leaving the end of a jump ramp with a speed of 15 m/s. At his highest point in the air the skier has a speed of 13 m/s. Ignoring air resistance, determine the skier's height H above the top of the ramp at the highest point of the jump. Select one: A. 3.14 m B. 2.86 m C. 2.20 m D. 5.71 m E. 0.102 m
Ornithologists have determined that some species of birds tend to avoid flights over large bodies of water during daylight hours. It is believed that more energy is required to fly over water than land because air generally rises over land and falls over water during the day. (i) A bird with these tendencies is released from an island that is 3 km from the nearest point B on a straight shoreline, flies to a point C on the shoreline, and then flies along the shoreline to its nesting area D. Points B and D are 10 km apart. Assume that the bird instinctively chooses a path that will minimize its energy expenditure. (Round your answers to two decimal places.) (a) In general, if it takes 1.2 times as much energy to fly over water as land, to what point C should the bird fly in order to minimize the total energy expended in returning to its nesting area? km from B (b) Let W and L denote the energy (in joules) per kilometer flown over water and land, respectively. Assuming the bird's energy expenditure is minimized, determine a function for the ratio WL in terms of x, the distance from B to C. W/L = (c) What should the value of W/L be in order for the bird to fly directly to its nesting area D? (d) If the ornithologists observe that birds of a certain species reach the shore at a point 2 km from B, how many times more energy does it take a bird to fly over water than land?
Use the model for projectile motion, assuming there is no air resistance and g = 32 feet per second per second. A baseball player at second base throws a ball 90 feet to the player at first base. The ball is released at a point 5 feet above the ground with an initial speed of 50 miles per hour and at an angle of 17∘ above the horizontal. At what height (in ft) does the player at first base catch the ball? (Round your answer to three decimal places.) feet
A projectile is launched from the top of a 20−m tall cliff towards another cliff that is 40−m tall and 100−m away. If the projectile is launched at an angle of 50∘, at what speed must it be launched to just barely reach the other cliff? (15 pts)
Three spiders are resting on the vertices of a triangular web. The sides of the triangular web have a length of a = 0.57 m, as depicted in the figure. Two of the spiders (S1 and S3) have +4.0 μC charge, while the other (S2) has −4.0 μC charge. (a) What are the magnitude and direction of the net force on the third spider (S3)? magnitude N direction ∘ counterclockwise from the +x-axis (b) Suppose the third spider (S3) moves to the origin. Would the net force on the third spider (S3) be greater than, less than, or equal to the magnitude found in part (a)? greater than in part (a) less than in part (a) equal to the part (a) (c) What are the magnitude and direction of the net force on the third spider (S3) when it is resting at the origin? magnitude N direction - counterclockwise from the +x-axis
A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. The height H of the slide is 8.0 m. a) At what velocity the person leaves the slide? Ans: 9.9 m/s b) As the drawing shows, how far from the edge of the slide does the person land on the water? Ans: 0.72 m [Hint: Use the conservation energy for the first part and use the appropriate kinematic equation for the second part]
A metal sphere hangs from a string and has 4 kg of mass. The sphere has a charge of +5.5 μC. A uniform electric field is turned on and directed to the right. (a) Which way does the sphere move? left right (b) What is the electric force on the metal sphere if the magnitude of the electric field is 106 N/C? N (c) When the sphere reaches equilibrium, what is the angle that the string makes with the vertical axis (assuming the same electric field as part (b))? 。
Two swimmers A and B, of weight 190 lb and 125 lb, respectively, are standing still at opposite ends of a 300 lb floating raft. If swimmer A starts moving toward the center of the raft at a speed of 2 ft/s relative to the raft while B moves to the right toward the end of the raft at 3 ft/s relative to the raft, what is the speed of the raft? Vc = −1.228
A 22 kg chimpanzee hangs from the end of a horizontal, broken branch of length L0 = 1.6 m, as shown in the figure(Figure 1). The branch is a uniform cylinder 4.2 cm in diameter, and the end of the branch supporting the chimp sags downward through a vertical distance Δx = 16 cm. Figure 1 of 1 Part A What is the shear modulus for this branch? Express your answer using two significant figures. Submit Request Answer
A sort of "projectile launcher" is shown in Fig. 20-52. A large current moves in a closed loop composed of fixed rails, a power supply, and a very light, almost frictionless bar touching the rails. A magnetic field is perpendicular to the plane of the circuit. The bar has a length of 20 cm, a mass of 1.5 g, and is placed in a field of 1.7 T. Figure 20-52. (a) What constant current flow is needed in order for it to accelerate to 28 m/s in a distance of 1.0 m ? A (B) In what direction must the field point? downwards upwards
What is the net charge on a sphere that has the following? (a) 5.27×106 electrons and 7.69×106 protons C (b) 235 electrons and 104 protons C
A dart gun includes a spring of spring constant k = 14 N/m which is used to fire a dart of mass m. The dart leaves the gun at a speed of v = 6.1 m/s after the spring is compressed 1 cm. 33% Part (a) What is the weight, Fg in Newtons, of the dart? Fg = Part (b) What is the dart's speed when it hits the floor vf, in m/s, if it is fired horizontally at a height of h = 2 meters? Part (c) What angle, θ in degrees, does the dart's final velocity make with the horizontal?
A member of a swim team is training by swimming in a river. The river is flowing uniformly at a constant speed of 2.50 m/s between parallel banks 70.0 m apart. The swimmer can only swim at a constant speed of 1.40 m/s. (a) The member of a swim team first chooses to minimize the amount of time spent in the water. Find the direction (in degrees), relative to the flow of the river, in which the swimmer must head to accomplish this. ० from the direction of the stream (b) How far (in m) downstream will the swimmer be carried? m (c) The member of a swim team returns to the original starting point, and next decides to minimize the distance he is carried downstream. Find the new direction (in degrees), relative to the flow of the river, in which the swimmer must head to accomplish this. ० from the direction of the stream (d) Now how far (in m) downstream will the swimmer be carried? m
A person pushes a 24.6-kg shopping cart at a constant velocity for a distance of 16.7 m on a flat horizontal surface. She pushes in a direction 33.3∘ below the horizontal. A 35.5-N frictional force opposes the motion of the cart. (a) What is the magnitude of the force that the shopper exerts? Determine the work done by (b) the pushing force, (c) the frictional force, and (d) the gravitational force.
A swimmer, capable of swimming at a speed of 1.40 m/s in still water (i.e., the swimmer can swim with a speed of 1.40 m/s relative to the water), starts to swim directly across a 1.85-km-wide river. However, the current is 1.17 m/s, and it carries the swimmer downstream. (a) How long does it take the swimmer to cross the river? (b) How far downstream will the swimmer be upon reaching the other side of the river? (a) Number Units (b) Number Units
The swimmer shown in the figure exerts an average horizontal backward force of 75.0 N with his arm during each 1.80 m long stroke. (a) What is his work output (in J) in each stroke? J (b) Calculate the power output (in W) of his arms if he does 100 strokes per minute. W
A 55.0-g toy car is released from rest on a frictionless track with a vertical loop of radius R. The initial height of the car is h = 4.20R. (a) What is the speed of the car at the top of the vertical loop? (Use the following as necessary: R and g.) v = (b) What is the magnitude of the normal force acting on the car at the top of the vertical loop?
An a-particle has a charge of +2 e and a mass of 6.64×10−27 kg. It is accelerated from rest through a potential difference that has a value of 1.93×106 V and then enters a uniform magnetic field whose magnitude is 2.29 T. The a-particle moves perpendicular to the magnetic field at all times. What is (a) the speed of the a-particle, (b) the magnitude of the magnetic force on it, and (c) the radius of its circular path? (a) Number Units (b) Number Units (c) Number Units
Swimmers at a water park have a choice of two frictionless water slides, as shown in the figure. Although both slides drop over the same height h, slide 1 is straight while slide 2 is curved, dropping quickly at first and then leveling out. How does the speed v1 of a swimmer reaching the bottom of slide 1 compare with v2, the speed of a swimmer reaching the end of slide 2 ? Slide 1 v1 > v2 v1 = v2 v1 < v2 The heavier swimmer will have a greater speed than the lighter swimmer, no matter which slide he uses. No simple relationship exists between v1 and v2.
The figure shows a swimmer at distance D = 32.0 m from a lightning strike to the water, with current I = 78.0 kA. The water has resistivity 30 Ω⋅m, the width of the swimmer along a radial line from the strike is 0.900 m, and his resistance across that width is 8.00 kΩ. Assume that the current spreads through the water over a hemisphere centered on the strike point. What is the current through the swimmer? Number Units
Three resistors with resistances R1 = R/2 and R2 = R3 = R are connected as shown, and a potential difference of 265 V is applied across terminals a and b (see figure below). (a) If the resistor R1 dissipates 88.0 W of power, what is the value of R? Ω (b) What is the total power supplied to the circuit by the emf? W (c) What is the potential difference across each of the three resistors? ΔV1 = V ΔV2 = V ΔV3 = V
You are on the Pirates of the Caribbean attraction in the Magic Kingdom at Disney World. Your boat rides through a pirate battle, in which cannons on a ship and in a fort are firing at each other. While you are aware that the splashes in the water do not represent actual cannonballs, you begin to wonder about such battles in the days of the pirates. Suppose the fort and the ship are separated by 89.0 m. You see that the cannons in the fort are aimed so that their cannonballs would be fired horizontally from a height of 6.60 m above the water. (a) You wonder at what speed (in m/s) they must be fired in order to hit the ship before falling in the water. (Enter the minimum speed.) m/s (b) Then, you think about the sludge that must build up inside the barrel of a cannon. This sludge should slow down the cannonballs. A question occurs in your mind: if the cannonballs can be fired at only 50.0% of the speed found earlier, is it possible to fire them upward at some angle to the horizontal so that they would reach the ship? Yes No
A water slide is constructed so that swimmers, starting from rest at the top of the slide, leave the end of the slide traveling horizontally. As the drawing shows, one person hits the water 5.00 m from the end of the slide in a time of 0.500 s after leaving the slide. Ignoring friction and air resistance, calculate the height H in the drawing. [Answer: H = 6.33]
A swimmer having mass of 55 kg is diving in a swimming pool has an effective body area of 0.76 m2 as shown in Fig. 1. The tension in the direction of swimmer's leg is 1.5 kN when the legs make an inclination of 30∘ with the vertical direction. If the swimmer's hands bend about 40∘ with the flow of water and the magnitude of wave is 2.5 m/s. Determine the lift and drag forces and their coefficients and discuss on the results. Fig: 1
You discover a new type of microscopic, atom-like object. The energy levels for this object are given by En = E1/n, where E1 = −20.0 eV. For this new object, determine the following. (a) excitation energy (in eV) of the object in the third excited state eV (b) amount of energy (in eV ) required to cause an object in the third excited state to become unbound eV (c) maximum number of different energy photons emitted as the object de-excites from the third excited state to the ground state (assuming all available transitions are possible) (d) maximum and minimum wavelength photons (in nm ) emitted when the object de-excites from the third excited state to the ground state λmax = nm λmin = nm nm
A water-skier is moving at a speed of 10.6 m/s. When she skis in the same direction as a traveling wave, she springs upward every 0.539 s because of the wave crests. When she skis in the direction opposite to that in which the wave moves, she springs upward every 0.427 s in response to the crests. The speed of the skier is greater than the speed of the wave. Determine (a) the speed and (b) the wavelength of the wave. (a) Number Units (b) Number Units
A projectile is launched from the ground with velocity |v→| = 4 m/s, at an angle θ = 64∘ from the horizontal direction. The projectile would have landed on the ground at the horizontal distance d1 away from the launch point, but instead it hit the top of a platform of height h in the way. The platform was hit at a horizontal distance d2 away from the launch point. What is the distance d1 in meters? Note that d1 is the distance that the projectile was supposed to travel if it had returned back to the ground. Use g = 9.8 m/s2 and retain one decimal place for you answer.
The figure below shows a resistor of resistance R = 3.00 Ω resistor connected to an ideal 12.0 V battery by means of two copper wires. Each wire has length 21.0 cm and radius 1.00 mm. In dealing with such circuits, we generally neglect the potential differences along wires and the transfer of energy to thermal energy in them. Check the validity of this neglect for the circuit by answering the following questions. (a) What is the potential difference across the resistor? (Enter your answer to 6 significant figures for comparison.) (b) What is it across each of the two sections of wire? mV (c) At what rate is energy lost to thermal energy in the resistor? W (d) At what rate is it lost in each of the two sections of wire? W
Consider the laser cavity below. Use d = 2.0 m and R2 = 1.0 m. Assume that M1 is a planar mirror. Figure 3: Schematic for Q3. (a) Show that the cavity is unstable. (b) Suppose that a ray starts out moving to the right at M1, at a height of 1 mm and parallel to the optical axis. Determine how many passes the ray will make through the cavity before it misses one of the mirrors.
The springs shown in the figure have spring constants of k = 10 N/m. When a current is established through the wire as shown, the magnetic force on the wire causes it to compress the springs by 1.0 cm. What is the current, I For full credit, you will need to include a free-body diagram in your answer.
A 10.0 cm long wire is pulled along a U-shaped conducting rail in a perpendicular magnetic field. The total electrical resistance of the wire and the rail is 0.20 Ω. Pulling the wire at a steady speed of 4.0 m/s causes 4.0 W of power to be dissipated in the circuit. (a) How big is the pulling force? (b) What is the strength of the magnetic field?
A particle with mass m and charge q moves in a region of space with uniform electric and magnetic fields (E→ = E0k and B→ = B0H). If the initial velocity of the particle is given by v→(0) = v0i^, determine the speed of the particle as a function of time, V(t). This is a challenging problem and you will not be penalized if you skip it.
The cylinder in (Figure 1) has a moveable piston attached to a spring. The cylinder's cross-section area is 10 cm2, it contains 0.0044 mol of gas, and the spring constant is 1500 N/m. At 20∘C the spring is neither compressed nor stretched. Figure 1 of 1 Part A How far is the spring compressed if the gas temperature is raised to 130∘C ? Express your answer with the appropriate units. View Available Hint(s) Δx = Value Units Submit Previous Answers
Figure 3 shows the projectile motion of a 1 kg cannonball launched at 20 meters per second. If the target for the cannonball is at 20 meters, what is the angle to the nearest whole degree, needed for the cannon launch? Enter your answer in the box.
A salamander of the genus Hydromantes captures prey by launching its tongue as a projectile: The skeletal part of the tongue is shot forward, unfolding the rest of the tongue, until the outer portion lands on the prey, sticking to it. The figure shows the acceleration magnitude a versus time t for the acceleration phase of the launch in a typical situation. The indicated accelerations are a2 = 415 m/s2 and a1 = 145 m/s2. What is the outward speed of the tongue at the end of the acceleration phase? Number Units
Figure (a) applies to the spring in a cork gun (Figure (b)); it shows the spring force as a function of the stretch or compression of the spring. The spring is compressed by 7.00 cm and used to propel a 3.50 g cork from the gun. (a) What is the speed of the cork if it is released as the spring passes through its relaxed position? (b) Suppose, instead, that the cork sticks to the spring and stretches it 1.90 cm before separation occurs. What now is the speed of the cork at the time of release? Force (N) (b) (a)
A spring with an unstrained length of 0.076 m and a spring constant of 2.0 N/m hangs vertically downward from the ceiling. A uniform electric field directed upward fills the region containing the spring. A sphere with a mass of 5.5×10−3 kg and a net charge of +6.4 μC is attached to the lower end of the spring. The spring is released slowly, until it reaches equilibrium. The equilibrium length of the spring is 0.059 m. What is the magnitude of the external electric field? Unstrained spring Spring with charged sphere and electric field
Two bags of equal mass m are tied together with unstretchable, massless rope. One bag hangs vertically, while the other is free to slide on a frictionless slope of angle β. Treat the tip of the slope (which the rope is passing over) like a massless, frictionless pulley. Let g denote the magnitude of free-fall acceleration. Let down define the positive direction for the hanging bag. What is ay, the vertical component of the acceleration of the hanging bag? ay = Enter your expression in terms of given quantities and integers.
Three point charges are located at the corners of a right triangle as shown in the figure. How much work does it take for an external force to move the charges apart until they are very far away from one another?
Pictures show the graph for electric potential energy (U) of two charges versus their separation (r). Select the proper graph for unlike charges. (b)
The drawing shows three identical springs hanging from the ceiling. Nothing is attached to the first spring, whereas a 4.5−N block hangs from the second spring. A block of unknown weight hangs from the third spring. From the drawing, determine (a) the spring constant (in N/m) and (b) the weight of the block hanging from the third spring. (a) Number Units (b) Number Units
A 10 kg box resting on a horizontal surface is attached to a 14 kg block by a thin light rope that passes over a frictionless pulley. The coefficient of kinetic friction between the horizontal surface and the 10 kg box is 0.25. The pulley has a shape of a uniform solid disk of mass 5 kg and a radius of 35 cm. After the system is released 10 kg box moves to the right, 14 kg block moves down, and the pulley rotates clockwise. Find: (a) the magnitude of the tension (in N) of the rope on the end attached to 10 kg box; (b) the magnitude of the tension (in N) of the rope on the end attached to 14 kg block; (c) the magnitude of the acceleration (in m/s2) of the 10 kg box; (d) the magnitude of the angular acceleration of the pulley (in rad/s2).
Learning Goal: Static and Kinetic Friction Short Calclations A 25.0 kg wooden crate rests on a wood floor. The coefficient of static friction between the wood crate and the wood floor is μs = 0.53. The coefficient of kinetic friction between the wood crate and the wood floor is 0.44. You pull on the rope attached to the crate. The magnitude of the gravitational acceleration is 9.80 m/s2. Part A - What maximum force (in Newtons) can you exert horizontally on the crate without moving it? Part B - If you pull on the crate with a 38.96 N horizontal force, what is the magnitude of the frictional force? Part C - Now you increase the pulling force gradually to the value in Part A, the crate will start moving. Notice that the type of frictional force will change and the magnitude will also change. After the crate starts moving, your pulfing force remains at the value in Part A. What will be the crate's acceleration? As shown in the same crate from the above parts rests on the same wooden floor. A 100 N force presses on the crate from above. Part D - What is the magnitude of the normal force on the crate by the floor? Part E - What is the minimum horizontal pulling force (in Newtons) to make the crate start moving?
A cylinder is fitted with a piston, beneath which is a spring, as in the drawing. The cylinder is open to the air at the top. Friction is absent. The spring constant of the spring is 3300 N/m. The piston has a negligible mass and a radius of 0.036 m. (a) When the air beneath the piston is completely pumped out, how much does the atmospheric pressure cause the spring to compress? (b) How much work does the atmospheric pressure do in compressing the spring? (a) Number Units (b) Number Units
In the figure, two particles, each with mass m = 0.79 kg, are fastened to each other, and to a rotation axis at O, by two thin rods, each with length d = 5.7 cm and mass M = 1.3 kg. The combination rotates around the rotation axis with angular speed ω = 0.31 rad/s. Measured about O, what is the combination's (a) rotational inertia and (b) kinetic energy? (a) Number Units (b) Number Units
In a judo foot-sweep move, you sweep your opponent's left foot out from under him while pulling on his gi (uniform) toward that side. As a result, your opponent rotates around his right foot and onto the mat. The figure shows a simplified diagram of your opponent as you face him, with his left foot swept out. The rotational axis is through point O. The gravitational force F→g on him effectively acts at his center of mass, which is a horizontal distance d = 25 cm from point O. His mass is 84 kg, and his rotational inertia about point O is 65 kg⋅m2. What is the magnitude of his initial angular acceleration about point O if your pull F→a on his gi is (a) negligible and (b) horizontal with a magnitude of 300 N and applied at height h = 1.4 m? Assume free-fall acceleration to be equal to 9.81 m/s2. (a) Number Units (b) Number Units
A box of mass 100 kg is sitting on a surface that that has an angle of inclination of 20 degrees. The coefficient of kinetic friction between the surface and the box is 0.1 and the coefficient of static friction is 0.35. What force must be applied up the ramp to just prevent the box from sliding down the incline. Assume that down the incline is the +x direction. a) 38.7 N b) 13 N c) 59.2 N d) 97.4 N e) 0.35 N
A small block of mass m = 3.25 kg is fired with an initial speed v0 = 4 m/s along a horizontal section of frictionless track, as shown in the top portion of the figure. The block then moves along the frictionless semicircular vertical track of radius R = 0.5 m. Part 1 Determine the force exerted by the track on the block at point A. F = Part 2 The bottom of the track consists of a horizontal section (L = 14 m) with friction. Determine the coefficient of kinetic friction between the block and the bottom portion of the track if the block just makes it to point B before coming to rest. μk = number (rtol = 0.05, atol = 1 e−08)
An infinite, nonconducting sheet has a surface charge density σ = +8.09 pC/m2. (a) How much work is done by the electric field due to the sheet if a particle of charge q0 = 8.01×10−19 C is moved from the sheet to a point P at distance d = 3.20 cm from the sheet? (b) If the electric potential V is defined to be zero on the sheet, what is V at P? (a) Number Units (b) Number Units
A ball is released from a height of 13 m and weighs 51 N. What is the magnitude |ΔU| of the total change in potential energy when the ball falls to the ground? |ΔU| =
As shown in the figure below, a green bead of mass 40 g slides along a straight wire. The length of the wire from point ( ) to point (B) is 0.800 m, and point (A) is 0.500 m higher than point (B). A constant friction force of magnitude 0.0400 N acts on the bead. (a) If the bead is released from rest at point (A), what is its speed at point (B) m/s (b) A red bead of mass 40 g slides along a curved wire, subject to a friction force with the same constant magnitude as that on the green bead. If the green and red beads are released simultaneously from rest at point (A), which bead reaches point (B) with a higher speed? the green bead the red bead both beads arrive with equal speed Explain.
Two blocks of equal mass are sliding on an inclined plane, as shown in the image below. At t = 0 s, the blocks are moving towards each other with equal speeds. A short while later, the blocks collide elastically and bounce off of one another. Which graph correctly describes how the center of mass (C.O.M.) velocity of the two-block system changes over time? Assume both blocks remain on the ramp for the duration of the time shown on the graph. Neglect drag and friction. The positive direction is defined as up the incline, as shown on the image above. B. C. D.
A student is completing various experiments using a wooden block in different scenarios. In which of the following scenarios is the block-earth system considered to be an open system? Neglect drag. Select two answers. A. The block is pushed across a floor at an increasing speed. B. The block slides across a rough floor. C. The block falls from the top of a building. D. The block slides across a frictionless surface.
A projectile is launched from ground level to the top of a cliff which is 195 m away and 135 m high (as shown in the figure( Figure 1)). If the projectile lands on top of the cliff 6.8 s after it is fired, find the initial velocity of the projectile ( (a)magnitude and (b)direction ). Neglect air resistance. Figure 1 of 1 Landing point v0 135 m
A spring is rigidly attached to a wall. At the end of the spring there is a charge +17 μC. On a separate wall there are three charges fixed a distance 0.8 m apart. All of the charges are equal in magnitude. The central negative charge is a distance 1.53 m from the final position of the charge attached to the spring. You can ignore any effect due to mass. Has the spring stretched or compressed from it's equilibrium length (the length it would have if there are no charges)? stretched compressed How much has the spring stretched/compressed from it's equilibrium position if the spring constant of the spring is 10 N/m mm.
A mass of 0.4 kg hangs motionless from a vertical spring whose length is 0.83 m and whose unstretched length is 0.59 m. Next the mass is pulled down to where the spring has a length of 1.04 m and given an initial speed upwards of 1.2 m/s. What is the maximum length of the spring during the motion that follows? maximum length = m
A body (1) of mass m1 = 1 kg is released from rest from a height of h1 = 1 m. It then travels down the frictionless ramp, and collides at position A with another body (2) of mass m2 = 4 kg. The coefficient of restitution e = 0.8. Find: a) the (vertical) height h2 up the ramp that body 1 (the 1 kg mass) rebounds to after the collision (insert below) b) the velocity vector of the 4 kg body after the collision (show on worksheet)
While entering a freeway, a car accelerates from rest at a rate of 2.24 m/s2 for 12.2 s. To help with this question, draw a sketch of the situation and list the knowns in this problem. a) How far does the car travel in those 12.2 s? m b) What is the car's final velocity? m/s
The figure shows a simple model for an Ice breaking operation. The coefficients of static and kinetic friction for contact between the ship's bow and ice are 0.08 and 0.060 , respectively, and the ship produces a thrust of 106 lb. Assume the ship makes contact with the Ice only on Its bow, and neglect all forces between the ship's hull and water except for the thrust. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. Determine the normal and friction forces acting on each side of the ship's bow as it moves through the ice field with constant velocity. (Round the final answers to four decimal places.) The normal force is ×106 Ib. The friction force is ×104 lb.
A student takes a strand of copper wire and forms it into a circular loop of circumference of 0.375 m. The student then places the loop in a uniform, constant magnetic field of magnitude 0.00303 T that is oriented perpendicular to the face of the loop. Pulling on the ends of the wire, they reduce the circumference of the loop to 0.147 m in a time interval of 0.572 s. Assuming that the loop remains circular as it shrinks, what is the magnitude of the average emf E induced around the loop during this time interval? |E| = V
The four particles shown below are connected by rigid rods of negligible mass where y1 = 6.30 m. The origin is at the center of the rectangle. The system rotates in the xy plane about the z axis with an angular speed of 6.50 rad/s. (a) Calculate the moment of inertia of the system about the z axis. kg⋅m2 (b) Calculate the rotational kinetic energy of the system. J
A suspended platform of negligible mass is connected to the floor below by a long vertical spring of force constant k = 1200 N/m. A circus performer of mass m = 70 kg falls from rest onto the platform from a height of h = 5.8 m above it, as shown below. Initially, the spring is not compressed or stretched. For this problem, define your system to consist of the person, platform, spring, and Earth, and you should take the reference point y = 0 to be the initial height of the platform. Part (a) Determine the total mechanical energy for this system. Is it conserved? Defend your reasoning. Part (b) As the performer falls, consider the following two segments of their descent: (i) from the moment the performer starts moving until they reach the platform, and (ii) from the moment they start compressing the platform until they reach a maximum compression. For each of two segments, describe what happens to the kinetic energy, gravitational potential energy, and spring potential energy in the system. You should be specific about what forms of energy are present and how they are being converted from one to another.
A ballistic of mass m = 100 g is traveling at a speed v towards a box of mass M = 1 kg sitting at rest. The ballistic collides with and sticks to the box, and the two move as a single body with a speed v1 along a rough, horizontal surface. The coefficient of friction between the box and the surface is μk = 0.33. Following the collision, the two objects travel a distance D = 8 m before coming to rest. See the figure below. Part (a) Is the mechanical energy of the ballistic-box system conserved during the collision? Defend your reasoning with a conceptual argument. Part (b) Determine the initial speed v at which the ballistic was traveling. For this question, you must use the concepts of work, energy, and momentum in order to receive full credit. Part (c) Suppose instead, after the collision, the ballistic-block system slides up an incline (μk is still 0.33). In order for the ballistic-box system to still travel a distance of 8 m, would the ballistic's initial speed need to be larger or smaller? You should provide a conceptual argument; no math or calculations are necessary.
Two students, Tom and Jerry, are jumping off a diving board into a swimming pool. Tom just drops straight downward off the board, and Jerry runs off the same board with some horizontal velocity vo. a) Which diver, Tom or Jerry, has the greater splashdown speed? Or are they the same? b) Calculate the splashdown speed for each diver, if the height of the board is 10 m, and Jerry's initial velocity is vo = 4.5 m/s.
A block of mass m is attached to the end of a weightless spring and placed on a frictionless horizontal surface. When the spring is compressed through a distance Δx from its unstretched length, it exerts a force F on the block. The block is released from rest from the position shown in the diagram. What is the speed of the block when the spring returns to its unstretched length? A. FΔx 2m B. FΔx m C. 2FΔx m D. 2 FΔx m
Two blocks, labeled A and B, are connected by a massless string that runs over a massless and frictionless pulley. Block A is sliding up along an inclined plane with ordinary surface friction. The string from block A runs over the pulley and then to block B which hangs straight down. At the start of the experiment, block A is sliding up the plane and block B is moving downward, both at a speed of v0 = 1.5 m/s. Block A has a mass of 3.3 kg. Block B has a mass of 1.4 kg. The plane is inclined at an angle of 27 degrees above horizontal. The coefficient of kinetic friction between block A and the plane is 0.36 (no units). Assume that the only significant forces on the blocks are normal forces, tensions forces, friction from the inclined plane, and gravity (with g = 9.81 m/s2 ). From the start of the experiment, when block A is sliding up the plane at a speed of 1.5 m/s, how far (in units of meters) does block A slide before coming to a stop? Just one more "show your work" after this one. You will need to submit your solution for this question.
A small bead with a mass m = 15.0 g slides along the frictionless wire form shown in the figure. The three heights hA = 6.60 m, hB = 5.40 m, and hC = 2.90 m are all measured from the floor. The bead is released from rest at point A. (a) What is the speed of the bead at points B and C? vB = m/s (b) What is the net work done on the bead by the force of gravity as it moves from point B to C?
15-51. The 20−kg package has a speed of 1.5 m/s when it is delivered to the smooth ramp. After sliding down the ramp it lands onto a 10−kg cart as shown. Determine the speed of the cart and package after the package stops sliding on the cart. Prob. 15-51
A 9.48-kg box is sliding across the horizontal floor of an elevator. The coefficient of kinetic friction between the box and the floor is 0.381. Determine the kinetic frictional force that acts on the box when the elevator is (a) stationary, (b) accelerating upward with an acceleration whose magnitude is 1.07 m/s2, and (c) accelerating downward with an acceleration whose magnitude is 1.07 m/s2. (a) Number Units (b) Number Units (c) Number Units
A uniform ladder stands on a rough floor and rests against a frictionless wall as shown in the figure. Since the floor is rough, it exerts both a normal force N1 and a frictional force f1 on the ladder. However, since the wall is frictionless, it exerts only a normal force N2 on the ladder. The ladder has a length of L = 4.9 m, a weight of WL = 67.5 N, and rests against the wall a distance d = 3.75 m above the floor. If a person with a mass of m = 90 kg is standing on the ladder, determine the following. (a) the forces exerted on the ladder when the person is halfway up the ladder (Enter the magnitude only.) N1 = N N2 = N f1 = N (b) the forces exerted on the ladder when the person is three-fourths of the way up the ladder (Enter the magnitude only. ) N1 = N N2 = N f1 = N
Block A is sliding down inclined side of the wedge B, as shown in the figure. The wedge has acceleration aB = 5 [m/s2] and the relative acceleration of block A with respect to wedge is aA∣B = 3 [m/s2] as shown in figure below. The inclination angle of the wedge is α = 35∘. Q7: Determine the magnitude of acceleration of block A, aA [m/s2]. Q8: Determine direction of acceleration of block A, β [deg].
A 15.0-g conducting rod of length 1.30 m is free to slide downward between two vertical rails without friction. The ends of the rod maintain electrical contact with the rails. The rails are connected to a 6.50−Ω resistor, and the entire apparatus is placed in a 0.430−T uniform magnetic field. Ignore the resistance of the rod and rails. What is the terminal velocity of the rod? m/s