The three objects in the drawing are connected by strings that pass over massless and friction-free pulleys, and are all initially at rest. The coefficient of static friction between the middle object and the surface of the table is 0.15 , while the coefficient of kinetic friction is 0.12 . What is the acceleration (in m/s2) of the middle object? a. 0, the middle object does not start moving due to the static friction. b. 0.047 c. 0.60 d. 0.46 e. 1.28
A thin, light wire is wrapped around the rim of a wheel, as shown in (Figure 1). The wheel rotates without friction about a stationary horizontal axis that passes through the center of the wheel. The wheel is a uniform disk with radius 0.276 m. An object of mass 4.10 kg is suspended from the free end of the wire. The system is released from rest and the suspended object descends with constant acceleration. For related problem-solving tips and strategies, you may want to view a Video Tutor Solution of An unwinding cable ii. Figure 1 of 1 Part A If the suspended object moves downward a distance of 2.85 m in 1.89 s, what is the mass of the wheel? Express your answer with the appropriate units. M =
A 8 kg block is hanging from a 5 kg moving pulley. The system starts from rest at State 1. Between State 1 and State 2 a constant 100 N force is applied to the end of the cable. What is the speed of the block after it has moved up by 0.8 m? Ignore friction in the system, the mass of the cable, and the mass of the small stationary pulley (but don't ignore the mass and size of the large moving pulley or the block). State 1 State 2 v1 = 0
A ski jumper of mass 70 kg is attempting to launch off the ramp below with a velocity of v = 90 km/h that points horizontally. This corresponds to v = 25 m/s. (a) (5 pts) Calculate the kinetic energy the ski jumper would have at the moment they launch off the ramp. (b) (10 pts) Ignoring friction and air resistance, you can assume that the sum of potential and kinetic energy for the jumper stays constant at all times. What is the height (above the dashed line) at which the skier has to start if the initial speed is zero?
A 62.0 kg skier is moving at 6.50 m/s on a frictionless, horizontal, snow-covered plateau when she encounters a rough patch 4.20 m long. The coefficient of friction between this patch and her skis is 0.30 . After crossing the rough patch and returning to friction-free snow, she skis down an icy, frictionless hill 2.50 m high. A. How fast is the skier moving (in m/s) when she gets to point B? B. How fast is the skier moving (in m/s ) when she gets to point C? C. How much energy was lost due to friction in crossing the rough patch?
Work. A block of mass m = 2.00 kg is attached to a spring of force constant k = 500 N/m as shown on the right. The block is pulled to a position xi = 5.00 cm to the right of equilibrium and released from rest. There is friction between the surface and the block. The coefficient of friction between block and surface is μk = 0.350. (a) (3 pts) What is the work done by the elastic force during the displacement? (b) (2 pts) What is the work done by the kinetic friction on the block during its motion? (2 pts) (d) (5 pts) What is the speed of the block as it passes through the equilibrium position? Use work-kinetic energy theorem.
A projectile is launched from and returns to ground level, as the figure shows. There is no air resistance. The horizontal range of the projectile is measured to be R = 174 m, and the horizontal component of the launch velocity is v0x = 26.0 m/s. Find the vertical component v0y of the projectile.
A block of mass 1.5 kg is attached to a horizontal spring that has a force constant 1200 N/m as shown in the figure below. The spring is compressed 2.0 cm and is then released from rest. b (a) A constant friction force of 4.7 N retards the block's motion from the moment it is released. Using an energy approach, find the position x of the block at which its speed is a maximum. cm (b) Explore the effect of an increased friction force of 15.0 N. At what position of the block does its maximum speed occur in this situation? cm
Q.6. A small point-like piece of clay with mass m = 200 g is traveling at a constant velocity v→0 = (30 m/s) î towards a stationary cylindrical hoop of mass M = 2000 g and radius R = 50 cm that is free to rotate about its central axis which is at the center of the zy-plane. Before sticking to the hoop, the clay is traveling along a horizontal line a distance d = 23 R. The clay impacts and sticks to the hoop at point A. a. What is the angular momentum of the system L → 0 before the collision about the origin? (include unit vector direction) b. What is the moment of inertia of the system after the clay sticks to the rod? c. Find the angular speed ω just after the collision. d. What is the kinetic energy of the system just after the collision? e. At what vertical height y does point A momentarily stop?
Car bumpers are designed to limit the extent of damage to the car in the case of low-velocity collisions. Consider a 3.30 kip passenger car impacting a concrete barrier while traveling at a speed of 4.0 mph The car's bumper consists of a linear spring of constant k = 4.47 kip/in. in parallel with a shock-absorbing unit generating a nearly constant force of 700 lb. over 3.0 in. Find the spring and shock compression necessary to stop the car. (Note: a kip = 1000 lb) Answer needs to be in inches (in.)
Problem 1: A skier leaves a ramp of a ski jump with a velocity v0 = 10 m/sec, 15∘ above the horizontal. The skier lands on a slope of incline 50∘ at a distance L from the launching point. (a) What distance L does the skier travel down the slope? (b) How long is the skier in the air? In other words, what is t when the skier lands on the slope? t = 0 x0 = 0 y0 = 0 v0x = 10 cos15∘ v0y = 10 sin15∘ ax = 0 ay = −g
A box is sliding up an incline that makes an angle of 31.2∘ with respect to the horizontal. The coefficient of kinetic friction between the box and the surface of the incline is 0.186. The initial speed of the box at the bottom of the incline is 3.90 m/s. How far does the box travel along the incline before coming to rest? Number Units
Work and Energy The 250 g block is pushed against a spring at A and released from rest. Determine the smallest deflection of the spring for which the block travels around the loop BCDE without losing the contact with it. Neglect friction. The stiffness of the spring is k = 200 N/m.
A small solid ball is released from rest while fully submerged in a liquid and then its kinetic energy is measured when it has moved 3.60 cm in the liquid (if it moves). The figure gives the results after many liquids are used: The kinetic energy K is plotted versus the liquid density ρliq , and Ks = 1.70 J sets the scale on the vertical axis. What is the volume of the ball in m3?
Some mass spectrometers, as shown in the figure, use an electric field to give the incoming ions a certain known kinetic energy as they enter the magnetic field. Assume a magnetic field strength of 0.2 T. (a) If a certain ion carries a charge of 10 μC, has a mass of 0.7 g, and possesses an initial kinetic energy of 3.5× 10−7 J, what is the radius r of its circular path?
A 100 kg skier with an initial speed of 12.0 m/s coasts up a h = 2.50 m high rise as shown in the figure. Find her kinetic energy at the top, if the coefficient friction between her skies and and the snow is 0.5. Given that the distance traveled up the incline is 10 m, g = 10 m/s2, cos(53.2) = 0.6, and sin(53.2) = 0.8 A. −15000 J B. 1700 J C. 127000 J D. 17,000 J E. 23000 J
Consider a skier moving down a ski slope. The length of the ski slope is ℓ = 2000 m and the track makes an angle of Θ = 70∘ with the horizontal. If the skier starts at the top of the track with zero initial speed, determine the takeoff speed of the skier at the bottom of the track using: (a) the work-energy theorem (b) the conservation of energy principle (c) the equations of motion with kinematic relationships
(d) The skier shown in figure 5d below has a mass of 75 kg. If the slope is at 12∘ to the horizontal, (i) What force down the slope is he exerting? [16 marks] (ii) What would his acceleration down the slope be? [16 marks] If the kinetic coefficient of friction is 0.08, what angle of slope would you recommend for a beginners slope so that they ski at a constant velocity rather than accelerating. [12 marks]
A skier starts from rest and slides down the top of a frictionless hemisphere of Radius "r". At what angle "theta" will the skier lose contact with the surface?
In the figure, a T-bar ski tow pulls a skier up a hill inclined at 10∘ above horizontal. The skier starts from rest and is pulled by a cable that exerts a tension T at an angle of 30∘ above the surface of the hill. The mass of the skier is 60 kg and the effective coefficient of kinetic friction between the skis and the snow is 0.18. What is the maximum tension in the cable (in N) if the starting acceleration is not to exceed 4.90 m/s2?
A skier leaves the ramp of a ski jump with a velocity of v = 27.0 m/s at θ = 29.0∘ above the horizontal, as shown in the figure. The slope where she will land is inclined downward at ϕ = 50.0∘, and air resistance is negligible. (a) Find the distance from the end of the ramp to where the jumper lands. m (b) Find the velocity components just before the landing. (Let the positive x direction be to the right and the positive y direction be up.) vx = m/s vy = m/s
3.82 kg water skier is being accelerated by a ski boat on a flat ("glassy") lake. The coefficient of kinetic friction between the skier's skis and the water surface is μk = 0.34. (a) What is the skier's acceleration if the rope pulling the skier behind the boat applies a horizontal tension force of magnitude FT = 340 N to the skier (θ = 0∘)? (b) What is the skier's horizontal acceleration if the rope pulling the skier exerts a force of FT = 340 N on the skier at an upward angle θ = 14.5∘?
A skier is going down a hill (we will assume it is frictionless). The x-axis is parallel to the hill, and the y-axis is perpendicular to the hill. The skier's mass is 50 kg and the hill is at an angle of 30∘ above the horizontal (this will also be the angle between the y-axis and the weight force). Determine the normal force on the skier and the skier's acceleration. Use g = 10 m/s2 for this problem. 483 N and 5 m/s2 483 N and 6.7 m/s2 None of the others 433 N and 5 m/s2 433 N and 50 m/s2
A circus performer stands on a platform and throws an apple from a height of 43.0 m above the ground with an initial velocity v0→ as shown in the figure below. A second, blindfolded performer must catch the apple. If v0 = 27.0 m/s, how far from the end of the platform should the second performer stand? (Assume θ = 30.0∘.) m
A penguin of 7 kg stands at the edge of an ice cliff and dives into the ocean below. The penguin has an initial velocity of 5 ms−1 and at an angle of 60∘ with respect to the horizontal. The cliff is 15 m above the water level. Assume air resistance is negligible and take the value of the acceleration due to gravity as 9.81 ms−1. Calculate: a) The time it takes for the penguin to hit the water. [3 marks] b) The horizontal distance travelled by the penguin before hitting the water. [2 marks] c) The velocity of the penguin just before hitting the water. [3 marks] d) The momentum of the penguin in unit vector notation at the highest point (with respect to the water level) of its projectile. [2 marks] e) Supposed that upon splashing on the water, the magnitude of the vertical component of the velocity found in part (c) above is being reduced by half in 0.2 seconds while the horizontal component remained the same, determine the impulsive force experience by the penguin. [2 marks].
A stone is thrown upward from the top of a building at an angle of 30∘ to the horizontal and with an initial speed of 20.0 m/s. The point of release is 45.0 m above the ground. (a) How long does it take for the stone to hit the ground? (b) Find the stone's speed at impact. (c ) Find the range of the stone. (d) Write the displacement in vector notation: Δr→ = ? Group: How long does it take the stone to reach maximum height and what is its velocity (in unit vector notation) at maximum height?
The diagram shows a projectile being launched at a velocity of 1.0 km s−1 at an angle of 30∘ to the horizontal. Assume that g = 9.8 m s−2 and that air resistance is negligible. a What is the time of flight of the projectile? b What is the speed of the projectile at its maximum height? c Determine the acceleration of the projectile 1.0 s after it is launched.
The projectile precesses about the Z axis at a constant rate of ϕ = 15 rad/s when it leaves the barrel of launcher. Determine its spin ψ˙ and the magnitude of its angular momentum HG. The projectile has a mass of 1.5 kg and a radius of gyration about its axis of symmetry ( z axis) and about its transverse axes (x & y axes) as kz = 65 mm and kx = ky = 125 mm, respectively. Had to make you try one.
At time t = 0, a projectile is launched from ground level. At t = 2.00 s, it is displaced d = 54 m horizontally and h = 53 m vertically above the launch point. What are the (a) horizontal and (b) vertical components of the initial velocity of the projectile? (c) At the instant it reaches its maximum height above ground level, what is its horizontal displacement D from the launch point? (a) Number Unit (b) Number Unit (c) Number Unit
In a ballistic pendulum lab you got the data as mentioned below: Mass of the bullet (m) = 69.6 g Mass of pendulum bob (M) = 277.4 g Velocity of the bullet after being fired from gun = 7.0 m/s. Calculate the loss in KE in the inelastic collision. [Hint : first use the formula for conservation of linear momentum to get the velocity (after collision) of bullet-pendulum (m+M) system, then calculate KE ] 1.365 J 13.68 mJ 168.8 mJ 1.688 J
A projectile is launched from ground as shown in the figure below. If hmax = 31 m and the angle the launch velocity makes with the horizontal is θ = 40∘, determine the flight time of the projectile. Take g = 9.81 m/s2 and express your answer in units of seconds with one decimal place.
A projectile is launched from the top of a platform of height h = 0.3 meters, with velocity |v→| = 1 m/s, at an angle θ = 43 degrees from the horizontal direction. How much time (in seconds) will it take for the projectile to reach the ground below the platform? Retain 1 decimal place for your answer. Use g = 9.8 m/s2
Two seconds after being projected from ground level, a projectile is displaced 53 m horizontally and 60 m vertically above its point of projection. It lands later on the ground. The figure below shows the motion of the projectile assuming negligible air resistance.
The height (in ft ) of a projectile launched off a cliff over water is given by: h(t) = −16t2 + 555t + 150 where t is the time (in seconds) after launch. (a) What is the initial height of the projectile? Number ft (b) How high does the projectile travel? (round to 2 decimal places) Number ft (c) When does the projectile hit its maximum height? (round to 2 decimal places) after Number seconds
A projectile is launched from ground level at an angle of 12.0∘ above the horizontal. It returns to ground level. To what value should the launch angle be adjusted, without changing the launch speed, so that the range doubles? Concept Simulation 3.2 reviews the general principles in this problem.
In the absence of air resistance, a projectile is launched from and returns to ground level. It follows a trajectory similar to that shown in Figure 3.10 and has a range of 26 m. Suppose the launch speed is doubled, and the projectile is fired at the same angle above the ground. What is the new range? Figure 3.10
A farm truck moves due east with a constant velocity of 8.80 m/s on a limitless, horizontal stretch of road. A boy riding on the back of the truck throws a can of soda upward (see figure below) and catches the projectile at the same location on the truck bed, but 19.0 m farther down the road. (a) In the frame of reference of the truck, at what angle to the vertical does the boy throw the can? ∘ (b) What is the initial speed of the can relative to the truck? m/s (c) What is the shape of the can's trajectory as seen by the boy? a straight line segment upward and then downward a symmetric section of a parabola opening downward An observer on the ground watches the boy throw the can and catch it. (d) In this observer's frame of reference, describe the shape of the can's path. a straight line segment upward and then downward a symmetric section of a parabola opening downward (e) In this observer's frame of reference, determine the initial velocity of the can. magnitude m/s direction ० above the horizontal eastward line
A model rocket takes off straight up. Its acceleration during the first 2 seconds of its motor burns is 20 m/s2. The model rocket continues as a projectile motion after the motor has burnt out. Neglect the aerodynamic drag. Figure 3 1.) determine the maximum altitude (height) the rocket reaches. 2.) determine the total time of flight from takeoff until the rocket hits the ground. 3.) determine the maximum velocity of the rocket during the flight.
The motor M is at rest when someone flips a switch and it starts pulling in the rope. The acceleration of the rope is uniform and such that it takes 0.50 s to achieve a retraction rate of 7.00 ft/s. Determine the tension in the rope during initial 0.50 s. The cargo C weighs 2576 Ib., the weight of the ropes and pulleys is negligible, and friction in the pulleys is negligible. Note: answer to be in pounds (Ib).
A 12.0 kg mass is placed on a 25.0∘ incline (θ = 25.0∘) and friction keeps it from sliding. The coefficient of static friction is 0.580 , and the coefficient of kinetic friction is 0.520 . What is the frictional force (if any) acting while the mass is at rest on the incline? (Take up the incline to be the positive direction.) −118 N +73.5 N −27.7 N +49.7 N −55.4 N
Figure 1 shows the potential energy associated with a conservative force F(x). A particle of mass m1 = 1 kg is undergoing F(x) and no other forces. The mechanical energy of the system is 9 J. (a) What is the sign of the force as a function of x? (b) Where are the turning points of the system (if any)? (c) where are the equilibrium points of the system (if any)? are they stable? Figure 1: Potential energy of a conservative (d) what is the velocity of the particle force F(x). at x = 4 m ? Describe the motion of a second particle of mass m2 = 2 kg with initial velocity v0 = −1 ms−1 and initial position x0 = 3 m. Exercise 1: Potential and Kinetic Energy (6 points)
A 10 kg ball A moving horizontally at 12 m/s collides with a 10 kg block B. The coefficient of restitution of the impact is 0.4 and the coefficient of kinetic friction between the block and the inclined surface is 0.5. Calculate the impulse made by the impulsive normal that produces the impact, the speed of the two bodies A and B after the impact and the distance that the block rises and how long it takes to stop.
Two objects are connected by a light string passing over a light, frictionless pulley as shown in the figure below. The object of mass m1 = 4.00 kg is released from rest at a height h = 3.80 m above the table. (a) Using the isolated system model, determine the speed of the object of mass m2 = 3.00 kg just as the 4.00−kg object hits the table. m/s (b) Find the maximum height above the table to which the 3.00−kg object rises. m
A block of mass m = 2.00 kg is attached to a spring of force constant k = 565 N/m as shown in the figure below. The block is pulled to a position xi = 5.75 cm to the right of equilibrium and released from rest. (a) Find the speed the block has as it passes through equilibrium if the horizontal surface is frictionless. m/s (b) Find the speed the block has as it passes through equilibrium (for the first time) if the coefficient of friction between block and surface is μk = 0.350. m/s
A 5.60−kg block is set into motion up an inclined plane with an initial speed of vi = 7.40 m/s (see figure below). The block comes to rest after traveling d = 3.00 m along the plane, which is inclined at an angle of θ = 30.0∘ to the horizontal. (a) For this motion, determine the change in the block's kinetic energy. J (b) For this motion, determine the change in potential energy of the block-Earth system. J (c) Determine the friction force exerted on the block (assumed to be constant). N (d) What is the coefficient of kinetic friction?
A skier is standing motionless on a horizontal patch of snow. She is holding onto a horizontal tow rope, which is about to pull her forward (see Figure below). The skier's mass is 59 kg, and the coefficient of static friction between the skis and snow is 0.14. (a) Draw the free-body diagram of the skier (b) What is the magnitude of the maximum force that the tow rope can apply to the skier without causing her to move?
A skier starts at the top of a very large, frictionless snowball, with a very small initial speed, and skis straight down the side (Fig. P7.63). At what point does she lose contact with the snowball and fly off at a tangent? That is, at the instant she loses contact with the snowball, what angle α does a radial line from the center of the snowball to the skier make with the vertical? Figure P7.63
A skier leaves the ramp of a ski jump with a velocity of v = 15.0 m/s, θ = 14.0∘ above the horizontal, as shown in the figure. The slope where she will land is inclined downward at ϕ = 50.0∘, and air resistance is negligible. (a) Find the distance from the end of the ramp to where the jumper lands. m (b) Find the velocity components just before the landing. (Let the positive x direction be to the right and the positive y direction be up. vx = m/s vy = m/s (c) Explain how you think the results might be affected if air resistance were included? This answer has not been graded yet.
A 60.0 -kg skier starts from rest at point A in the Figure. The curvy slope is very icy and frictionless except for the section BC, of length 10.0 m that was previously groomed by a snow groomer. The skier skies down the slope and hits a rubber bumper that can be modeled as a spring with force constant k = 1.63×104 N/m. The skier compresses the bumper 0.300 m from its equilibrium position before coming to rest momentarily. a) List all conservative and non-conservative forces acting on the skier in this problem. b) Calculate the work done by kinetic friction. c) Calculate the stored potential energy in the bumper when it is compressed 0.300 m from its equilibrium position. d) Determine the coefficient of kinetic friction between the groomed surface BC and the skier.
The launching mechanism of a toy gun consists of a spring of unknown spring constant, as shown in the figure below. If the spring is compressed a distance of 0.130 m and the gun fired vertically as shown, the gun can launch a 18.0-g projectile from rest to a maximum height of 21.0 m above the starting point of the projectile. a (i) (a) Neglecting all resistive forces, describe the mechanical energy transformations that occur from the time the gun is fired until the projectile reaches its maximum height. (b) Neglecting all resistive forces, determine the spring constant. (c) Neglecting all resistive forces, find the speed of the projectile as it moves through the equilibrium position of the spring (where x = 0 ), as shown in Figure (b).
The skier shown in figure 5d below has a mass of 75 kg. If the slope is at 12∘ to the horizontal, (i) What force down the slope is he exerting? (ii) What would his acceleration down the slope be? If the kinetic coefficient of friction is 0.08 , what angle of slope would you recommend for a beginners slope so that they ski at a constant velocity rather than accelerating.
A 74.1-kg skier coasts up a snow-covered hill that makes an angle of 33.0∘ with the horizontal. The initial speed of the skier is 8.13 m/s. After coasting a distance of 1.52 m up the slope, the speed of the skier is 4.00 m/s. (a) Find the work done by the kinetic frictional force that acts on the skis. (b) What is the magnitude of the kinetic frictional force? (a) Number Units (b) Number Units
A circus performer stands on a platform and throws an apple from a height of 43 m above the ground with an initial velocity v0 as shown in the figure below. If v0 = 19 m/s and a 2 nd performer on the ground at d = 28.63 m happens to have caught the apple. (θ = 40∘.) At what angle (below horizontal) the apple hits the catcher? a. 40.0∘ b. 56.4∘ c. 65.2∘ d. 78.5∘ e. None of above is within 1∘ from the correct answer
A skier starts from rest at the top of a hill. The skier coasts down the hill and up a second hill, as the drawing illustrates. The crest of the second hill is circular, with a radius of 33.6 m. Neglect friction and air resistance. What must be the height h of the first hill so that the skier just loses contact with the snow at the crest of the second hill? Number Units
A projectile is launched at point O in the x−y plane with the initial velocity and angle, as shown. Simultaneously, an airplane is flying in x−y plane in a straight line at an angle of 30-deg from the x-axis with a constant velocity of 480 ft/s. At the instant of 4 -seconds after the launch of the ball, calculate the following: a) The magnitude of the resultant velocity of the ball as measured by the pilot, b) The direction (measured counterclockwise from the x-axis) of the resultant velocity of the ball as measured by the pilot.
A projectile is launched from the ground with velocity |v→| = 3 m/s, at an angle θ = 54∘ 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.
A projectile is launched from and returns to ground level, as the figure shows. There is no air resistance. The horizontal range of the projectile is measured to be R = 166 m, and the horizontal component of the launch velocity is v0x = 20.0 m/s. Find the vertical component v0y of the projectile. Number Units
Projectile Motion in Two Dimensions: A young girl tosses two toys through the air at different times. Both tosses hurl the toys at an initial 30∘ angle with the horizontal. One toy lands in the pool just at its near edge, B, and the other at its far edge, C. Both toys land at the exact same instant. Determine: (A) the time of flight for each toy (B) the time in between the two tosses (C) the initial speed of each toy (D) the velocity of each toy (magnitude and direction) the instant they strike their respective edge.
Write a code that will determine the maximum height achieved by a projectile as well as its overall range, as illustrated in Figure 1, when it is fired at an angle of θ = 45∘ and an initial velocity of v0 = 25 m/s. Some pertinent formulas are given in the figure, though you will need to solve the expressions to come up with a formula for maximum height/range (or refer to a Physics I text for additional information). Print the results of the computation to the console for the user to read, including the following information: a. Maximum height achieved by the projectile. b. Maximum range achieved by the projectile. Figure 1: Projectile motion problem
A model rocket is launched from rest with a constant upward acceleration of 3 m/s2 under the action of a small thruster, Figure 1. The thruster shuts off after 8 seconds, and the rocket continues upward until it reaches its apex. At apex, a small chute opens which ensures that the rocket falls at a constant speed of 0.85 m/s until it impacts the ground. Determine the maximum height h attained by the rocket and the total flight time. Neglect aerodynamic drag during ascent, and assume that the mass of the rocket and the acceleration of gravity are both constant. Figure 1
A skier going down a 25 degree slope is accelerating at a rate of 1.0 m/s2 in the direction down the slope. a. Draw a free body diagram for the skier. All forces should be labeled as weights (w or Fg), normal forces (n), kinetic friction forces (fk), static friction forces (fs), or tensions (T). Subscripts are not needed. (3 points) b. Assuming air drag is negligible, find the coefficient of kinetic friction between the skier and the slope. Show all your work so I can follow your reasoning. (7 points)
A 1.46-kg rock is released from rest at a height of 15.5 m. Ignore air resistance and determine (a) the kinetic energy at 15.5 m, (b) the gravitational potential energy at 15.5 m, (c) the total mechanical energy at 15.5 m, (d) the kinetic energy at 0 m, (e) the gravitational potential energy at 0 m, and (f) the total mechanical energy at 0 m. (a) Number Units (b) Number Units (c) Number Units (d) Number Units (e) Number Units (f) Number Units
Required information An electromagnetic rail gun can fire a projectile using a magnetic field and an electric current. Consider two horizontal conducting rails that are 0.510 m apart with a 46.8 g g conducting projectile that slides along the two rails. A magnetic field of 0.760 T is directed upward. A constant current of 1.90 A passes through the projectile. If the coefficient of kinetic friction between the rails and the projectile is 0.350, how fast is the projectile moving after it has traveled 8.20 m down the rails? m/s
A projectile is fired from the edge of a cliff as shown in the figure at an angle of 30∘ above the horizontal. The cliff is 20 m high. The initial velocity is 13.4 m/s. The projectile reaches maximum height at point P and then falls and strikes the ground at point Q. How far from the base of the cliff does the projectile land (in m)? Neglect air resistance and use g = 9.81m s2 as the magnitude of the acceleration due to gravity.
An extreme skier takes off from a jump and is going for height. If she leaves the jump traveling 15 m/s, and is traveling 11.9 m/s as she reaches the top of her flight, how high does she get above the top of the ramp? Assume g ≈ 10 m/s2.
(a) For a skier moving horizontally on level snow what is the magnitude of the normal force on the skier with a weight of 710 N and a speed of 25 m/s ? |Fn| = N. On the ski jump sketched on the left, the surface of the ski jump is horizontal at its lowest part. However, there is a vertical acceleration required for the skier to change direction which we call the centripetal acceleration. So at the lowest point, the normal force must balance gravity and provide the centripetal force that changes the direction of the skier. (b) For a ski jump with radius, R = 85 m. What is the magnitude of the normal force on the skier with a weight of 710 N and a speed of 25 m/s at the bottom of the ski jump? (Assume the very bottom of the ski jump is horizontal.) |Fn| = N. (c) What is the work done by the normal force on the skier while traveling on the curved part with radius 85 m ? Work = J
A projectile is launched from the ground as shown in the figure below with an initial speed of vo = 45 m/s with θ = 62∘ and lands on the landing point shown. If X = 32 m, determine the height of the landing point. Take g = 9.81 m/s2 and express our answer in units of meters using one decimal place.
A physics experiment involves the launching of a projectile from an Olympic Bob Sled track. The projectile is an empty Bob Sled, with a mass of 180 kg. The Sled starts moving from rest at the location labeled "A" on the diagram shown below. (There is no friction.) a) What is the Total Energy of the Sled at Location-A? b) What is the Launch Velocity of the Sled? c) At maximum height in flight, how high above the ground is the sled?
The 0.1−1 b projectile A is subjected to a drag force of magnitude kv2, where the constant k = 0.002 lb−sec2/ft2. This drag force always opposes the velocity v. At the instant depicted, v = 100 ft/sec, θ = 45∘, and r = 400 ft. Determine the corresponding values of r and θ.
A ship maneuvers to a position at a horizontal distance Δx1 = 2.50×103 m from an island's mountain peak with maximum height hM = 1.80×103 m, and fires a projectile at an enemy ship on the other side of the peak, which is at a horizontal distance Δx2 = 6.10×102 m from the peak, as illustrated below. The projectile is shot with an initial velocity vi = 2.50×102 m/s at an angle θ = 75.0∘. Assume no air resistance and ay = −g = −9.80 m/s2. a) What type of motion does the projectile undergo? What type of trajectory does it have? b) Find the maximum height hmax reached by the projectile. c) Find the total time of flight in the air Δttot just before the projectile hits the water surface. d) How close horizontally to the enemy ship does the projectile land? e) How close vertically does the projectile come to the peak?
The golfer shown in the figure above has a tall tree (obstacle) in the path of his goal. The tree is 80 m away from the golfer and is 12 m tall. a) Given that the golfer hits the ball at an initial velocity of 45 m/s, at an angle of 20 degrees to the horizontal, determine if the ball would clear the tree. b) A second golfer is faced with a similar challenge, but he instead hits the ball at an initial angle of 30 degrees to the horizontal. Determine the minimum initial velocity that the second golfer must hit the ball to ensure that the ball just clears the tree. c) Calculate the velocity and corresponding angle to the horizontal at the point where the second golfer's ball just clears the tree.
A projectile is launched from point A with v0 = 30 m/s and θ = 35∘. Determine the x- and y- coordinates of the point of impact. The equation of parabola is y = kx2.
Billiards is an activity that involves a lot of physics. In the collision below, the billiard balls all have identical masses of 0.23 kg. Make the following two determinations: a) Was momentum conserved in the collision? Justify your answer with calculated values. Note: to answer this you will have to look at velocity and total momentum in both the x-direction and y-direction, before and after the collision. [4 marks] b) Was kinetic energy conserved in the collision? Justify your answer with calculated values. [3 marks]
A radar tracks the flight of a projectile (see Figure P3.6). At time t, the radar measures the horizontal component vx(t) and the vertical component vy(t) of the projectile's velocity and its range R(t) and elevation ϕ(t). Are these measurements sufficient to compute the horizontal distance D from the radar to the launch point of the projectile? If so, derive the expression for D as a function of g and the measured values vx(t), vy(t), R(t), and ϕ(t).
A 17-g bullet is shot vertically into an 5−kg block. The block lifts upward 5.0 mm (see the figure). The bullet penetrates the block and comes to rest in it in a time interval of 0.0010 s. Assume the force on the bullet is constant during penetration and that air resistance is negligible. The initial kinetic energy of the bullet is closest to (A) 36 J (B) 72 J (C) 8.3×10−4 J (D) 49 J (E) 0.25 J
The coefficient of friction is 0,25 between both surfaces of the thin, light plate shown in the figure below. Determine the tension in the wire holding the 15 kN block to the wall and then calculate the magnitude of the smallest force P required to start movement of the plate.
Figure (a) shows a circular disk that is uniformly charged. The central z axis is perpendicular to the disk face, with the origin at the disk. Figure (b) gives the magnitude of the electric field along that axis in terms of the maximum magnitude Em at the disk surface. The z axis scale is set by zs = 27.0 cm. What is the radius of the disk? (a) (b) Number Units