The bob of a simple pendulum of length I = 40 in. is released from rest when θ = 5∘. Assuming simple harmonic motion, determine the magnitudes of the velocity and acceleration of the bob after the pendulum has been in motion for 1.75 s. The magnitude of the velocity of the bob after the pendulum has been in motion for 1.75 s is ft/s. The magnitude of the acceleration of the bob after the pendulum has been in motion for 1.75 s is ft/s2. NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part.
In a pinball machine, a ball of mass 120 gram is placed in front of a horizontal spring of spring constant k = 90 N/m. The spring is pulled so that it squeezes by x = 5 cm, and then let go. The ball then rises up a ramp. Assume no rotation of the ball, what will be the speed of the ball when it has travelled L = 63 cm along the incline. The ramp is at an angle of θ = 8 degrees. Ignore friction.
Ball 1 is launched with an initial vertical velocity v1 = 133 ft/sec. Ball 2 is launched 2.6 seconds later with an initial vertical velocity v2. Determine v2 if the balls are to collide at an altitude of 215 ft. At the instant of collision, is ball 1 ascending or descending? Answer: v2 = ft/sec
A mass-less spring having a spring constant k = 300 N/m, and length 30.0 cm is laid on a horizontal table. Its left end is rigidly attached to a fixed wall. The other end has a point mass of 0.6 kg attached to it. At equilibrium, this mass is at position shown as MP. The mass (and spring) is pulled to the right, so that the mass is now at point A which is 9 cm from the mean position (MP), and held there. The mass is then released. It accelerates towards the mean position, and then goes past it, and compresses the spring. The coefficient of kinetic friction between the mass and the table is 0.15 . Calculate the speed of the mass as it crosses the point marked 'B', which is 4 cm from the mean position. Write your answer in m/s.
A tennis ball of mass (75 g) is placed on top of a basketball of mass (590 g), both balls are freed from rest and at the same time fall to a height of (1.2 m) as shown in the figure. Calculate the speed of the basketball when it reaches the ground. Assuming that the collision is elastic with the ground, calculate the height that the tennis ball reaches.
A block of mass 3.3 kg is attached to a string that passes over a pulley. The block is initially held at rest, and then pulled by a force F = 84 N to the right, as shown in the figure. The pulley is like a disk of mass 0.6 kg and radius 0.8 cm, and is frictionless. What will be the kinetic energy of the block when it has moved up a distance 2.2 m?
Consider the two small, equal-mass, charged balls shown in the figure. The top ball is suspended from the ceiling by a thread, and has a charge of q1 = 31.4 nC. The bottom ball has a charge of q2 = −58.0 nC, and is directly below the top ball. Assume d = 2.00 cm and m = 6.90 g. (a) Calculate the tension (in N) in the thread. N (b) If the thread can withstand a maximum tension of 0.180 N, what is the smallest value d can have before the thread breaks? (Give your answer in cm.) cm
In the figure, a solid 0.3 kg ball rolls smoothly from rest (starting at height H = 6.1 m) until it leaves the horizontal section at the end of the track, at height h = 2.4 m. How far horizontally from point A does the ball hit the floor? Number Units
Concept Simulation 5.1 reviews the concepts that are involved in this problem. A child is twirling a 0.0291-kg ball on a string in a horizontal circle whose radius is 0.0511 m. The ball travels once around the circle in 0.364 s. (a) Determine the centripetal force acting on the ball. (b) If the speed is doubled, by what factor does the centripetal force increase? (a) Number Units (b) Number Units
At a picnic, there is a contest in which hoses are used to shoot water at a beach ball from three directions. As a result, three forces act on the ball, F1→, F2→, and F3→ (see the drawing). The magnitudes of F1→ and F2→ are F1 = 89.0 newtons (N) and F2 = 84.0 N. Determine (a) the magnitude of F3→ and (b) the angle θ such that the resultant force acting on the ball is zero. (a) Number Units (b) Number Units
Bob has just finished climbing a sheer cliff above a level beach and wants to figure out how high he climbed. All he has to use is a baseball, a stopwatch, and a friend on the ground below with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is about v0 = 31.7 m/s. Bob starts the stopwatch as he throws the ball, with no way to measure the ball's initial trajectory, and watches carefully. The ball rises and then falls, and after t1 = 0.710 s the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball hit the ground x = 129 m from the base of the cliff. How high h above the beach was the ball when it was thrown? h =
Bob has just finished climbing a sheer cliff above a beach and wants to figure out how high he climbed. All he has to use, however, is a baseball, a stopwatch, and a friend on the ground with a long measuring tape. Bob is a pitcher, and knows that the fastest he can throw the ball is v0 = 76.0 mph, Bob starts the stopwatch as he throws the ball (with no way to measure the ball's initial trajectory) and watches carefully. The ball rises and then falls, and after t1 = 0.910 s, the ball is once again level with Bob. Bob cannot see well enough to time when the ball hits the ground. Bob's friend then measures that the ball landed a distance of x = 376 ft. from the base of the cliff. The gravitational acceleration in imperial units is 32.2 f/s2. How tall hc is the cliff if Bob threw the ball from exactly 5 ft above the cliff edge? hc =
(b) A block of mass 0.45 kg is at rest on the top of a plane inclined at 20∘ to the horizontal. A bullet of mass 0.05 kg moving at 100 ms−1 parallel to the plane strikes the upper part of the block and gets embedded in it and the two travel together down the plane. Use the laws of conservation of momentum and energy to determine: i) How fast the bullet and block will be travelling before reaching bottom of the plane. [3] ii) The coefficient of friction between the block and plane. [7]
A box (mass m ) is released from rest and slides down an inclined rough surface. The friction interaction results in an increase in thermal energy of the two surfaces (box and incline) of Efric ( > 0). The incline of height H makes an angle θ with respect to the horizontal. This problem should be solved using energy methods, not F→net = ma→. A. [6 pts] Find a symbolic expression for the speed of the block when it gets to the bottom of the incline, vbot. Your answer should be in terms of the given quantities m, H, θ, Efric and constants. Some symbols may not be needed. B. [2 pts] D. Does your result make sense if the height of the incline is larger/smaller? "Yes" or "No" is not sufficient. Explain the behavior you expect and whether your result shows that. C. [2 pts] Does your result make sense if there is no friction? "Yes" or "No" is not sufficient. Explain the behavior you expect and whether your result shows that.
The 60−N weight object initially at rest slides down the smooth ramp and is stopped by the spring. The static friction coefficient between the object and the ramp is μk = 0.10. If the object is to remain 0.6 m away from the point of contact (this means shortening the spring by 0.6 m) what is the required spring constant k ? [40 P]
The figure shows a 4.00-kg box being released from rest to slide down a frictionless track of height h = 2.73 m. (Note this image is not to scale. ) Determine the following. (a) the speed of the box vbottom at the bottom of the track m/s (b). its. speed v at a height of y = 1.15 m above the bottom of the track m/s. Question 5.3 b: A football is thrown from an initial height of 1.75 m above the ground. The football's initial velocity components are vxi = 6.90 m/s and vyi = 5.35 m/s. Determine the football's maximum height above the ground. Ignore air resistance and any other nonconservative forces. m
(a) A child of mass m is released from rest at the top of a water slide, at height 'h', 8.5 m above the bottom of the slide as shown in figure 6 . Assuming that the slide is frictionless because of the water on it, find the child's speed at the bottom of the slide. 5 marks figure 6
A 50 kg block sits at rest on a table. A student presses firmly downward on the block at an angle of 25∘ below horizontal with a force of 250 N. The coefficients of static and kinetic friction are 0.5 and 0.2 respectively. a. Does the block begin to move? b. If yes, what is its acceleration? If no, what is the frictional force acting on the block?
A block released from rest at position A slides with negligible friction down an inclined track, around a vertical loop, and then along a horizontal portion of the track, as shown above. The block never leaves the track. After the block is released, in which of the following sequences of positions is the speed of the block ordered from fastest to slowest?
Two men (A & B), having weights of 120.0 lbs. and 150.0 lbs. , respectively, stand on a 300.0 lb. cart initially at rest. Each runs at a speed of 5.0 ft/s relative to the cart. Determine the speed of the cart if man A runs and jumps off, causing the cart to move with man B, and then man B jumps off the same end.
Q1 - The car starts from rest at t = 0 and travels along a straight line with the speed described by the graph. Construct the displacement and acceleration vs time (s−t and a−t) for the time interval 0 ≤ t ≤ 40 sec.
3/151 The system is released from rest with the spring initially stretched 2 in. Calculate the velocity of the 100−lb cylinder after it has dropped 6 in. Also determine the maximum drop distance of the cylinder. Neglect the mass and friction of the pulleys. Problem 3/151
A block of mass m = 4.00 kg, starting from rest, slides down a frictionless inclined plane (ramp) of length 3.00 m. The plane is inclined by an angle of θ = 25.0∘ to the ground. At the bottom of the plane, the block slides along a rough horizontal surface with a coefficient of kinetic friction μk = 0.200 until it comes to rest. Let y = 0 represent a position along this horizontal surface. a) What is the initial mechanical energy (kinetic plus potential) of the object? b) What is the speed of the block when it reaches the bottom of the ramp? c) What is the work done by the friction force? d) What is the magnitude of the friction force on the horizontal surface? e) How far does the object slide along the horizontal surface before stopping?
Starting from rest, the motorboat travels around the circular path, ρ = 50 m, at a speed v = (0.8t)m/s, where t is in seconds. (Figure 1) Figure 1 of 1 Part A Determine the magnitude of the boat's velocity when it has traveled 30 m. Express your answer with the appropriate units. Submit Request Answer Part B Determine the magnitude of the boat's acceleration when it has traveled 30 m. Express your answer with the appropriate units. Submit Request Answer
You are riding a broomstick and see a golden ball hovering motionless 37 m above you and 17 m in front of you. The ball suddenly begins dropping in free-fall with no forces acting on it besides gravity. You accelerate instantaneously (i. e. you instantly reach your maximum velocity) and fly at a constant velocity in a straight horizontal direction. What must your velocity be to catch the golden ball? Assume the gravity acts at 9.81 m/s2 and that this problem does not violate any copyright laws. Figure not to scale. The next question will provide you with space to show your work.
The mass of ball A is 1 kg. The mass of ball B is 1.5 kg. The mass of ball C is 1.8 kg, if ball A has a speed of 2 m/s just before a direct collision with B, and balls B and C are at rest. If the coefficient of restitution between A and B is e = 0.8. The speed of ball B after collision is 1.2 m/s 8 m/s 3.5 m/s 17 m/s 25 m/s
Two bowling balls are at rest on top of a uniform wooden plank with their centers of mass located as in the figure below. The plank has a mass of 4.70 kg and is 1.00 m long. Find the horizontal distance (in m) from the left end of the plank to the center of mass of the plank-bowling balls system. m
A small ball is projected horizontally as shown and bounces at point A. Determine the range of initial speed v0 for which the ball will ultimately land on the horizontal surface at B. The coefficient of restitution at A is e = 0.8 and the distance d = 4 m. Problem 3/268
The 5.4−kg cylinder is released from rest in the position shown and falls on the spring, which has been initially precompressed 50 mm by the light strap and restraining wires. If the stiffness of the spring is 5.3 kN/m, compute the additional deflection δ of the spring produced by the falling cylinder before it rebounds.
In the figure here, a solid brass ball of mass 0.211 g will roll smoothly along a loop-the-loop track when released from rest along the straight section. The circular loop has radius R = 0.14 m, and the ball has radius r ≪ R. (a) What is h if the ball is on the verge of leaving the track when it reaches the top of the loop? (b) If the ball is released at height h = 5R, what is the magnitude of the horizontal force component acting on the ball at point Q?
In the arrangement of the figure, billiard ball 1 moving at a speed of 2.2 m/s undergoes a glancing collision with identical billiard ball 2 that is at rest. After the collision, ball 2 moves at speed 1.8 m/s, at an angle of θ2 = 37∘. What are (a) the magnitude and (b) the direction (angle θ1) of the velocity of ball 1 after the collision? (a) Number Units (b) Number Units
The cue gives the cue ball A a velocity parallel to the y axis. The cue ball hits the eight ball B and knocks it straight into the corner pocket. If the magnitude of the velocity of the cue ball just before the impact is 2 m/s and the coefficient of restitution is e = 1, what are the velocity vectors of the two balls just after the impact? (The balls are of equal mass.)
When the player releases the ball from rest at a height of 5 ft above the floor, it bounces to a height of 3.5 ft. If he throws the ball downward, releasing it at 3 ft above the floor, how fast would he need to throw it so that it would bounce to a height of 12 ft?
Billiard ball A is moving in the y-direction with a velocity of 2 m/s when it strikes ball B of identical size and mass initially at rest. Following the impact, the balls are observed to move in the directions shown. Calculate the velocities vA and vB which the balls have immediately after the impact. Treat the balls as particles and neglect any friction forces acting on the balls compared with the force of impact.
Two identical billiard balls can move freely on a horizontal table. Ball A has a velocity vo = 25 cm/s as shown and hits ball B, which is at rest, at a point C defined by θ = 30∘. Knowing that the coefficient of restitution between the two balls is e = 0.75, and assuming no friction, determine a. The speed of each ball after impact b. The angle between the balls after impact
The small ball of mass m and its supporting wire become a simple pendulum when the horizontal cord is severed. the ratio k is defined as ratio of the tension T in the supporting wire immediately after the cord is cut to that in the wire before the cord is cut. Determine the angular position θ where the ratio k becomes 1/2. Enter an answer in degrees up to the first decimal place.
In the figure here, a ball is thrown up onto a roof, landing 4.50 s later at height h = 22.0 m above the release level. The ball's path just before landing is angled at θ = 65.0∘ with the roof. (a) Find the horizontal distance d it travels. (Hint: One way is to reverse the motion, as if it is on a video.) What are the (b) magnitude and (c) angle (relative to the horizontal) of the ball's initial velocity?
Two identical billiard balls (mA = mB = 0.16 kg) can move freely on a horizontal table. Ball A has a velocity v→0 = 10 m/s→ and hits ball B, which is at rest, at a point C defined by θ = 30∘. The coefficient of restitution between the two balls is e = 0.9. Assume no friction. Determine: a. ) The velocity of each ball after impact (magnitude and angle with respect to horizontal of the page, don't forget to include the quadrant). b. ) The efficiency of the collision.
A tennis player strikes the tennis ball with her racket when the ball is at the uppermost point of its trajectory as shown. The horizontal velocity of the ball just before impact with the racket is v1 = 15 m/s and just after impact its velocity is v2 = 21 m/s directed at the 15∘ angle as shown. If the 60 g ball is in contact with the racket for 0.02 s, determine the magnitude of the average force R exerted by the racket on the ball. Also determine the angle β made by R with the horizontal.
Two smooth billiard balls A and B each have a mass of 0.2 kg. Ball A strikes ball B with velocity (vA)1 = 1.5 m/s as shown, where ball B is originally at rest and the collision can be assumed to be perfectly elastic (that is, the coefficient of restitution e = 1). Do the following: (a) find the final velocity of each ball just after the collision, and (b) draw a diagram of the two balls just after the collision showing the approximate direction that each is travelling.
Problem 17.102 A uniform cylinder of mass m and radius R is at rest on a sharp corner O with θ = 0. The cylinder is given a tiny nudge to the right, causing the cylinder to rotate about the corner. If the coefficient of static friction between the cylinder and the corner is μs, determine μs as a function of θ at which the cylinder slips. If μs = 14, determine the angle at which the cylinder slips. Figure P17.102 Answer μs = sinθ 7cosθ−4, θ = 30.51∘
A A small 0.10 kg block starts from rest at point A, which is at a height of 1.0 m. The surface between points A and B and between points C and D is frictionless, but is rough between points B and C, having a coefficient of friction of 0.10 . After traveling the distance ℓ = 1.0 m, the small block strikes a larger block of mass 0.30 kg, and sticks to it, compressing the spring to a maximum distance x = 0.50 m. Determine (a) the speed of the 0.10 kg block at point B. (b) the acceleration of the 0.10 kg block between points B and C. (c) the speed of the block at point C. (d) the speed of the combined small and large block immediately after they collide. (e) the spring constant of the spring.
Block A and Block B are initially at rest, with Block A on top of a floor inclined 30∘ from the horizontal, and Block B resting on top of Block A. The mass of Block A is 40.0 kg, and the mass of Block B is 15.0 kg. The friction between Block A and the inclined floor is negligible. A force P is applied to Block A, as shown in the figure. It was observed that when P exceeds 500 N, Block B slips with respect to Block A. [25%] Determine the acceleration of Block A when P is equal to 500 N. [25%] Determine the acceleration of Block B when P is equal to 500 N. [25%] Determine the Normal Force acting between Block A and Block B. [25%] Determine the coefficient of impending slide friction.
Three balls are attached by rigid rods of negligible mass as seen in the diagram below. This system is placed on a table which lies in the horizontal plane (noting that the view shown below is the "bird's eye" view of the table). Balls A and B each have a mass of 0.2 kg, while Ball C has a mass of 0.8 kg. Note that the diagram is not to scale. (a) Locate the x and y coordinates of the ball and rod system's centre of mass, G, within the coordinate system shown. (b) At the instant the 10 N force is applied as shown in the diagram, calculate the instantaneous linear acceleration of the mass centre. (c) At the instant the 10 N force is applied, calculate the instantaneous angular acceleration of the ball and rod system, α.
Boxes A and B are at rest on a conveyor belt that is initially at rest. The belt is suddenly started in an upward direction so that slipping occurs between the belt and the boxes. Knowing that the coefficients of kinetic friction between the belt and the boxes are (μk)A = 0.8 and (μk)B = 0.82, determine the initial acceleration of each box. The initial acceleration of box A, aA, is ft/s2. The initial acceleration of box B, aB, is ft/s2.
A soccer ball is kicked from the ground with an initial speed of 19.4 m/s at an upward angle of 42.1∘. A player 50.8 m away in the direction of the kick starts running to meet the ball at that instant. What must be his average speed if he is to meet the ball just before it hits the ground? Neglect air resistance. Use g = 9.81 m/s2. Number Unit
A crate of mass m is initially at rest at the highest point of an inclined plane which has a height of 6.83 m and has an angle of θ = 30.7∘ with respect to the horizontal. After it has been released, it is found to be traveling at v = 0.64 m/s a distance d after the end of the inclined plane, as shown. The coefficient of kinetic friction between the crate and the plane is μp = 0.1, and the coefficient of friction on the horizontal surface is μr = 0.2. Find the distance, d, in meters. d = m
An object of mass 34 m, initially at rest, explodes breaking into two fragments of mass m and 3 m, respectively. Which one of the following statements concerning the fragments after the explosion is true? The smaller fragment will have twice the speed of the larger fragment. The smaller fragment will have three times the speed of the larger fragment. They will fly off at right angles. They will fly off in the same direction. The larger fragment will have three times the speed of the smaller fragment.
A cylinder of mass M and radius R rolls without sliding under the action of force F. Calculate a) the acceleration of the cylinder's centre of mass b) the direction and measure of static friction and c) its speed when its centre of mass is displaced by a distance d. All answers will be a function of M, R, F taken as given.
X = 0 A person with mass m1 = 52 kg stands at the left end of a uniform beam with mass m2 = 105 kg and a length L = 3.3 m. Another person with mass m3 = 59 kg stands on the far right end of the beam and holds a medicine ball with mass m4 = 9 kg (assume that the medicine ball is at the far right end of the beam as well). Let the origin of our coordinate system be the left end of the original position of the beam as shown in the drawing. Assume there is no friction between the beam and floor. What is the location of the center of mass of the system? m Submit Help The medicine ball is throw to the left end of the beam (and caught). What is the location of the center of mass now? m Submit Help What is the new x-position of the person at the left end of the beam? (How far did the beam move when the ball was throw from person to person?) m Submit Help To return the medicine ball to the other person, both people walk to the center of the beam. At what x-position do they end up? m Submit Help
In the figure here, a ball is thrown up onto a roof, landing 3.90 s later at height h = 21.0 m above the release level. The ball's path just before landing is angled at θ = 55.0∘ with the roof. (a) Find the horizontal distance d it travels. (Hint: One way is to reverse the motion, as if it is on a video.) What are the (b) magnitude and (c) angle (relative to the horizontal) of the ball's initial velocity? (a) Number Unit (b) Number Unit (c) Number Unit
Determine the horizontal velocity vA of a tennis ball at A so that it just clears the net at B. Also, find the distance s where the ball strikes the ground.
The figure shows a 100 kg block being released from rest from a height of 1.0 m. It then takes it 8.255 s to reach the floor. Determine the mass m of the other block (in kg). The pulley has no appreciable mass or friction
An m1 = 2.0 kg steel ball is initially moving to the right at a velocity of v14 = +10 m/s. The ball strikes an m2 = 3.0 kg steel ball that is initially at rest. The collision is elastic. After the collision, the velocity of m1 is v1f = −2.0 m/s. (a) What is the velocity of m2 after the collision, i.e. v2f? (b) How much kinetic energy did the ball with mass m1 lose? Equation: (a) m1v1i + m2v2i = m1v1f + m2v2f (b) In general, kinetic energy, K = 12 mv2 (a) v2f = −6.0 m/s (b) KE lost = 54 J (a) v2f = +8.0 m/s (b) KE lost = 96 J (a) v2f = +4.0 m/s (b) KE lost = 96 J (a) v2f = +10 m/s (b) KE lost = 75 J (a) v2f = +7.0 m/s (b) KE lost = 84 J
A 0.6-kg ball A is moving with a velocity of magnitude 6 m/s when it is hit as shown by a 1-kg ball B which has a velocity of magnitude 4 m/s. Knowing that the coefficient of restitution is 0.8 and assuming no friction, determine the velocity of each ball after impact. (Round the final answer to three decimal places.) The velocity of ball A after impact is v′A = m/s ∘. The velocity of ball B after impact is v′B = m/s Z ∘.
The block started from rest and slides in a frictionless path. Calculate the value of cos(θ) when the system becomes at rest again after the block sticks to the rod. mass of the block, m = 0.06 kg. mass of the rod, M = 0.1 kg. Length of the rod, L = 0.59 m h = 0.23 m NOTE: Final answer in two decimal places. Use pi = 3.14. NO UNITS needed.
*13-76. Prove that if the block is released from rest at point B on a smooth path of arbitrary shape, the speed it attains when it reaches point A is equal to the speed it attains when it falls freely through a distance h; i. e. , v = 2 gh. Prob. 13-76
Kayla is bowling with her friends. Her bowling ball has a radius 4 inches long. After she releases the ball, it's possible to track the height of the finger hole above the ground. When the ball touches the ground, the finger hole is at the 12-o'clock position. As the ball moves down the lane, it has backspin and thus rotates counterclockwise based on the given diagram. Complete the definition for function f that represents the finger hole's height above the ground (in inches) in terms of the number of radians a the ball has rotated since it touched the ground. (Note that a is a number of radians swept out from the 12 -o'clock position.) f(a) =
Problem 11.023 - Dropped ball: Acceleration as a function of velocity NOTE: This is a multi-part question. Once an answer is submitted, you will be unable to return to this part. A ball is dropped from a boat so that it strikes the surface of a lake with a speed of 16.5 ft/s. While in the water, the ball experiences an acceleration of a = 10−0.8 v, where a and v are expressed in ft/s2 and ft/s, respectively. The ball takes 3.9 s to reach the bottom of the lake. Problem 11.023. a - Depth of lake: Obtaining velocity from acceleration, and position from velocity, by integration Determine the depth of the lake. The depth of the lake is ft. Problem 11.023. b - Speed at bottom: Obtaining velocity from acceleration by integration Determine the speed of the ball when it hits the bottom of the lake. The speed of the ball is ft/s.
The three blocks shown in the picture are at rest. The coefficient of friction between the 3.00 kg block on the table and the 2.00 kg on the ramp is the same. The block H has the maximum mass that keeps the system at rest. a) Solve for the coefficient of friction. (ans: μ = 0.471) b) Solve for the maximum mass of the Block H that keeps the system at rest. (ans: 2.27 kg)
When outfielders in baseball throw the ball towards the infield, they usually allow the ball to take one bounce, on the theory that it arrives sooner this way. Assume that, after the bounce, the ball rebounds at the same angle θ as before (as shown below), but loses half its speed. a. Assuming the ball is always thrown with the same speed, with what angle θ should the outfielder throw the ball in order to go the same distance as a ball thrown upward at 45∘ with no bounce? b. Determine the ratio of the times for the one-bounce, and no bounce throws. Hint: You will save a lot of work if you first solve the "general" problem of how far a ball launched at angle θ and speed vo will travel. That is, keep everything in terms of variables vo, g, and θ. Then consider each of the three cases individually, using the formula you just found.
Suppose the wheel with the ladybugs was now allowed to slow to rest as it continued to rotate in the counter-clockwise direction. The direction of bug2's linear acceleration is along the y-axis x-axis z-axis
An electron at rest of mass 9.11×10−31 kg is accelerated through a potential difference of 350 V. It then enters some deflecting plates of 50 V with dimensions as shown. Calculate the distance, x, or of the deflection of the electron. The charge on an electron is 1.6×10−19 C). (20 marks)
A 2.40 kg ball is attached to a spring and allowed to oscillate. The graph below shows the ball's position x as a function of time t. For this motion, find the . . . a) spring constant b) total energy c) ball's speed and acceleration at t = 2 s d) equation for the position of the ball at all times x(t)
A steel ball of mass 0.490 kg is fastened to a cord that is 69.0 cm long and fixed at the far end. The ball is then released when the cord is horizontal, as shown in the figure. At the bottom of its path, the ball strikes a 3.30 kg steel block initially at rest on a frictionless surface. The collision is elastic. Find (a) the speed of the ball and (b) the speed of the block, both just after the collision.
A particle initially has a speed of 0.43c. (Enter your answers in terms of c. Round your answers to at least three decimal places.) (a) At what speed does its momentum increase by 1%? c (b) At what speed does its momentum increase by 10%? c (c) At what speed does its momentum increase by 100%? c
Two smooth disks A and B each have a mass of 0.5 kg. Both disks are moving with the velocities shown when they collide. Suppose that (vA)1 = 6 m/s, (vB)1 = 5 m/s. Part A Determine the coefficient of restitution between the disks if after collision B travels along a line, 30∘ counterclockwise from the y axis. Express your answer using three significant figures. e =
An object of mass m1 = 0.145 kg undergoes uniform circular motion. The radius R of its circular path is 1.00 m. It is connected by a massless string through a hole in a frictionless table to a larger object of mass m2 = 0.285 kg, as shown in the figure. Assume that mass m2 remains stationary. Calculate the tension T in the string. T = N Calculate the linear speed v of the circular motion of mass m1. v = m/s
A cyclist travelling at 15 km/h changes velocity uniformly to 20 km/h in 1 min, maintains this velocity for 5 min and then comes to rest uniformly during the next 15 s. Draw a velocity/time graph and hence determine the accelerations in m/s2 (a) during the first minute, (b) for the next 5 minutes, and (c) for the last 10 s
Bonus: Investigate whether the equilibrium can be maintained. The coefficient of static friction is μs = 0.3. Hint: The friction at B is pointing up, determine the ratio F/N at B in terms of the distance x where x is the distance between the normal force line of action and the top surface of the block. Determine the possible range of x and if there are any values of x so that F/N < μs.
The figure shows a box of mass m = 4.65 kg pulled to the right across a horizontal surface by a constant tension force of magnitude T = 23.0 N. The tension force is inclined at an angle θ = 21.5∘ above the horizontal and the friction force has magnitude fk = 13.0 N. The box is pulled a distance d = 2.15 m. Determine the work done on the box by the tension force, the normal force, and the kinetic friction force. We'll use WT, Wn, and Wfk to represent the magnitudes of the tension, normal, and friction forces, respectively. WT = J Wn = J wfk =
A Mass of 500 kg pulled by a winch over an inclined plane. The coefficient of kinetic friction between the mass and the ramp is f = 0.3. R = 20 [cm] is the radius of the drum. 1) Find the Tension in the cable. 2) Find the Engine Torque needed to pull the mass. 3) If the drum rotates 1 (rotation per minute) Find the engine Power in Watt.
An object with mass m1 interacts with a second object m2 through a mutual attractive force. At the instant shown in the diagram below, object m1 has a velocity v1 while m2 has a velocity v2. Show that the total momentum of the system p = m1v1 + m2v2 does not change with time.
As a result of a glancing collision with the surface of the sphere (see Figure), the velocity of a small ball (mass m = 139 g, shown in green) changes from V0 = 7.0 m/s directed rightward to VF = 5.0 m/s directed 53.1∘ above the horizontal. The ball was in contact with the sphere for a time 0.20 s. [20 pts] What is the magnitude of the change in momentum of the ball?
You throw a 0.374 kg ball off the top of a 13.0 m tall building with an initial angle of 30.0∘ above the horizontal. The ball rises to a maximum height of 18.6 m before falling back to the ground. How much work does gravity do on the ball from the point you release the ball until it hits the ground? 47.6 J −47.6 J −68.2 J 68.2 J
A 2 kg ball is moving at 3 m/s to the right and hits a 3 kg ball moving to the left at 4 m/s. After the collision the two balls stick together. All this is happening on a level frictionless surface. Questions 28-31 refer to this situation. In this collision: Momentum is not conserved, KE is not conserved Momentum is conserved, KE is not conserved Momentum is conserved, KE is conserved Momentum is not conserved, KE is conserved
A 2 kg ball is moving at 3 m/s to the right and hits a 3 kg ball moving to the left at 4 m/s. After the collision the two balls stick together. All this is happening on a level frictionless surface. Questions 28-31 refer to this situation. This is an example of: A completely inelastic collision An elastic collision A partially inelastic collision
A boy tosses a ball onto the roof of a house. For the launch conditions shown, determine the slant distance s to the point of impact. Also, determine the angle θ which the velocity of the ball makes with the roof at the moment of impact. Answers: s = m θ =
The figure shows a thin rod, of length L = 1.50 m and negligible mass, that can pivot about one end to rotate in a vertical circle. A heavy ball of mass m−8.40 kg is attached to the other end. The rod is pulled aside to angle θ0 = 10∘ and released with initial velocity v0→ = 0. (a) What is the speed of the ball at the lowest point? (b) Does the speed increase, decrease, or remain the same if the mass is increased? (a) Number Units (b)
Consider the following figure. m = 50.0 kg (a) What force in newtons should the woman in the figure exert on the floor with each hand to do a push-up? Assume that she moves up at a constant speed. N (b) The triceps muscle at the back of her upper arm has an effective lever arm of 1.76 cm, and she exerts force on the floor at a horizontal distance of 18.4 cm from the elbow joint. Calculate the magnitude of the force in newtons in each triceps muscle. N Compare the magnitude of the total force exerted by both triceps muscles to her weight. total force exerted by both triceps muscles her weight = (c) How much work does she do in joules if her center of mass rises 0.260 m? (d) What is her useful power output in watts if she does 23 push-ups in one minute? W
Find the time required to pull the block, m = 10 kg (initially at rest), through a distance 20 m when μ = 0 (with friction) and μ = 0.25 (without friction). Hints: (i) Find the acceleration, a, of the block using, (ii) Find the time using, S = Ut + 0.5at2
The figure shows a person whose weight is W = 696 N doing push-ups. Find the normal force exerted by the floor on (a) each hand and (b) each foot, assuming that the person holds this position.
Problem: A woman of mass M = 60.0 kg is doing push-ups as shown in the figure. Her center of mass through which her weight, W acts downward is at a distance a = 1.60 m from her toes on which she rests. Her arms are at a distance b = 1.85 m from her toes. Magnitude of acceleration due to gravity, g = 10 m/s2. What is the magnitude of the upward force, F that her arms must exert to hold this position? 25. A 1294 N B 519 N C 694 N D 1119 N E 600 N
EXTRA CREDIT (5 points All or nothing - no partial credit) Suppose an object of mass m, initially travelling with a velocity v1, collides with an object of mass m initially at rest. Prove that the angle between the velocity vectors of the two objects of the two particles after the collision is 90 degrees.
In the figure R1 = 5.33 Ω, R2 = 10.07 Ω, R3 = 15.26 Ω, C1 = 5.21 μF, C2 = 10.23 μF, and the ideal battery has emf E = 23.1 V. Assuming that the circuit is in the steady state, what is the total energy stored in the two capacitors? Number Units
In the following figure, the horizontal surface is frictionless. The two forces acting on the block each have magnitude of 30 N and mass of the block is 10 kg. a) what is the magnitude of the resulting acceleration of the block? b) what is the magnitude of the normal force of the block?
An object with momentum p→ = ⟨4, −2, 10⟩ kg⋅m/s is acted on by a force F→ = ⟨110, 30, 80⟩ N, and your task is to calculate the parallel and perpendicular components of this force. A good check on your work is to see whether your calculated vectors for F→∥ and F→⊥ add up to F→. Also, since the angle between F→∥ and F→⊥ should be 90 degrees, F→∥⋅ F→⊥ should be zero (it won't be exactly zero, due to the finite precision of computer numbers). Calculate the component of the force that is parallel to the momentum: F→∥ = ⟨ ⟩ N
A 3.09 kg particle has a velocity of (3.07 i^ − 3.97 j^) m/s. (a) Find its x and y components of momentum. px = kg⋅m/s py = kg⋅m/s kg⋅m/s (b) Find the magnitude and direction of its momentum. kg⋅m/s (clockwise from the +x axis)
A child is at a point in her swing when the chain makes an angle of 60∘ with the upright. The tension in the chain is 480 N. Determine the horizontal and vertical components of the tension in the cable (acting on the child).
A 5.00 kg block is placed on top of a 10.0 kg block (Fig. above). A horizontal force of 45.0 N is applied to the 10 kg block, and the 5.00 kg block is tied to the wall. The coefficient of kinetic friction between all moving surfaces is 0.200 . (a) Draw a free-body diagram for each block and identify the action reaction forces between the blocks. (b) Determine the tension in the string and the magnitude of the acceleration of the 10.0 kg block.
In the figure an electric dipole swings from an initial orientation i(θi = 24.1∘) to a final orientation f(θf = 24.1∘) in a uniform external electric field E→. The electric dipole moment is 1.76×10−27 C⋅m; the field magnitude is 2.75×106 N/C. What is the change in the dipole's potential energy? Number Units
Two disks A and B have weights of 22.2 N and 8.9 N, respectively, slide on a smooth surface with the initial velocities shown in the figure. They impact at the origin with the line of impact shown. If the coefficient of restitution is 0.6 , determine the final velocities of each disk.
An aerialist on a high platform holds onto a trapeze attached to a support by an 7.6-m cord. (See the drawing.) Just before he jumps off the platform, the cord makes an angle of 44∘ with the vertical. He jumps, swings down, then back up, releasing the trapeze at the instant it is 0.67 m below its initial height. Calculate the angle θ that the trapeze cord makes with the vertical at this instant.