The spring in FIGURE EX10.22a is compressed by Îx. It launches the block across a frictionless surface with speed v 0 . The two springs in FIGURE EX10.22b are identical to the spring of Figure...
The spring in FIGURE EX10.23a is compressed by Îx. It launches the block across a frictionless surface with speed v 0 . The two springs in FIGURE EX10.23b are identical to the spring of Figure...
FIGURE EX10.25 is the potential-energy diagram for a 500 g particle that is released from rest at A. What are the particles speeds at B, C, and D? U (J) 5- 4 3 2- 0+ B D FIGURE EX10.25
In FIGURE EX10.28, what is the maximum speed a 200 g particle could have at x = 2.0 m and never reach x = 6.0 m? U (J) 16- 12 - 8- 4. 0+ x (m) FIGURE EX10.28 4 2.
A system in which only one particle can move has the potential energy shown in FIGURE EX10.30. What is the x component of the force on the particle at x = 5, 15, and 25 cm? U (J) 10- 0+ -x (cm) 40 T...
A system in which only one particle can move has the potential energy shown in FIGURE EX10.31. What is the y component of the force on the particle at y = 0.5 m and 4 m? U (J) 60 ry (m) 5 0- 2 FIGURE...
FIGURE EX10.28 shows the potential energy of a 500 g particle as it moves along the x-axis. Suppose the particle??s mechanical energy is 12 J. a. Where are the particle??s turning points?b. What is...
FIGURE EX10.34 shows the potential energy of a system in which a particle moves along the x-axis. Draw a graph of the force F x as a function of position x. U (J) 2- 04 FIGURE EX10.34
A particle moves from A to D in FIGURE EX10.35 while experiencing force F = (6iÌ + 8jÌ) N. How much work does the force do if the particle follows path (a) ABD, (b) ACD, (c) AD? Is this...
A force does work on a 50 g particle as the particle moves along the following straight paths in the xy-plane: 25 J from (0 m, 0 m) to (5 m, 0 m); 35 J from (0 m, 0 m) to (0 m, 5 m); 5 J from (5 m, 0...
A system loses 400 J of potential energy. In the process, it does 400 J of work on the environment and the thermal energy increases by 100 J. Show this process on an energy bar chart.
How much work is done by the environment in the process shown in FIGURE EX10.39? Is energy transferred from the environment to the system or from the system to the environment? E (J) 1,2.1 01 K; + U...
A very slippery ice cube slides in a vertical plane around the inside of a smooth, 20-cm-diameter horizontal pipe. The ice cubes speed at the bottom of the circle is 3.0 m/s. What is the ice cubes...
A 50 g ice cube can slide up and down a frictionless 30 slope. At the bottom, a spring with spring constant 25 N/m is compressed 10 cm and used to launch the ice cube up the slope. How high does it...
You have been hired to design a spring-launched roller coaster that will carry two passengers per car. The car goes up a 10-m-high hill, then descends 15 m to the tracks lowest point. Youve...
Its been a great day of new, frictionless snow. Julie starts at the top of the 60° slope shown in FIGURE P10.44. At the bottom, a circular arc carries her through a 90 turn, and she then launches...
A block of mass m slides down a frictionless track, then around the inside of a circular loop-the-loop of radius R. From what minimum height h must the block start to make it around without falling...
You have a ball of unknown mass, a spring with spring constant 950 N/m, and a meter stick. You use various compressions of the spring to launch the ball vertically, then use the meter stick to...
Truck brakes can fail if they get too hot. In some mountainous areas, ramps of loose gravel are constructed to stop runaway trucks that have lost their brakes. The combination of a slight upward...
Use work and energy to find an expression for the speed of the block in FIGURE P10.52 just before it hits the floor if (a) The coefficient of kinetic friction for the block on the table is k (b) The...
A system has potential energy U(x) = x + sin((2 rad/m)x) as a particle moves over the range 0 m x m. a. Where are the equilibrium positions in this range? b. For each, is it a point of stable or...
An object moving in the xy-plane is subjected to the force F = (2xy i + x 2 j) N, where x and y are in m. a. The particle moves from the origin to the point with coordinates (a, b) by moving first...
An object moving in the xy-plane is subjected to the force Fu = (2xy i + 3y j) N, where x and y are in m. a. The particle moves from the origin to the point with coordinates (a, b) by moving first...
Rank in order, from largest to smallest, the momenta (p x ) a to (p x ) e of the objects in FIGURE Q11.1. 20 g 20 g 200 g b 2 m/s 1 m/s 0.1 m/s 10 g 10 g 1 m/s 2 m/s FIGURE Q11.1
A 2 kg object is moving to the right with a speed of 1 m/s when it experiences an impulse of 4 N s. What are the objects speed and direction after the impulse?
What is the magnitude of the momentum of a. A 3000 kg truck traveling at 15 m/s? b. A 200 g baseball thrown at 40 m/s?
In FIGURE EX11.5, what value of F max gives an impulse of 6.0 N s? F, max 0+ 2 t (ms) 10 4 8. FIGURE EX11.5
FIGURE EX11.7 is an incomplete momentum bar chart for a 50 g particle that experiences an impulse lasting 10 ms. What were the speed and direction of the particle before the impulse? kg m/s -2 -4- J....
A sled slides along a horizontal surface on which the coefficient of kinetic friction is 0.25. Its velocity at point A is 8.0 m/s and at point B is 5.0 m/s. Use the momentum principle to find how...
Far in space, where gravity is negligible, a 425 kg rocket traveling at 75 m/s fires its engines. FIGURE EX11.11 shows the thrust force as a function of time. The mass lost by the rocket during these...
A 600 g air-track glider collides with a spring at one end of the track. FIGURE EX11.12 shows the gliders velocity and the force exerted on the glider by the spring. How long is the glider in contact...
A 5000 kg open train car is rolling on frictionless rails at 22 m/s when it starts pouring rain. A few minutes later, the cars speed is 20 m/s. What mass of water has collected in the car?
A 10,000 kg railroad car is rolling at 2.0 m/s when a 4000 kg load of gravel is suddenly dropped in. What is the cars speed just after the gravel is loaded?
A 10-m-long glider with a mass of 680 kg (including the passengers) is gliding horizontally through the air at 30 m/s when a 60 kg skydiver drops out by releasing his grip on the glider. What is the...
A 300 g bird flying along at 6.0 m/s sees a 10 g insect heading straight toward it at a speed of 30 m/s. The bird opens its mouth wide and enjoys a nice lunch. What is the birds speed immediately...
The parking brake on a 2000 kg Cadillac has failed, and it is rolling slowly, at 1.0 mph, toward a group of small children. Seeing the situation, you realize you have just enough time to drive your...
Fred (mass 60 kg) is running with the football at a speed of 6.0 m/s when he is met head-on by Brutus (mass 120 kg), who is moving at 4.0 m/s. Brutus grabs Fred in a tight grip, and they fall to the...
A 50 g ball of clay traveling at speed v 0 hits and sticks to a 1.0 kg brick sitting at rest on a frictionless surface. a. What is the speed of the brick after the collision? b. What percentage of...
package of mass m is released from rest at a warehouse loading dock and slides down the 3.0-m-high, frictionless chute of FIGURE EX11.25 to a waiting truck. Unfortunately, the truck driver went on a...
A 50 kg archer, standing on frictionless ice, shoots a 100 g arrow at a speed of 100 m/s. What is the recoil speed of the archer?
A 70.0 kg football player is gliding across very smooth ice at 2.00 m/s. He throws a 0.450 kg football straight forward. What is the players speed afterward if the ball is thrown at a. 15.0 m/s...
Dan is gliding on his skateboard at 4.0 m/s. He suddenly jumps backward off the skateboard, kicking the skateboard forward at 8.0 m/s. How fast is Dan going as his feet hit the ground? Dans mass is...
Two ice skaters, with masses of 50 kg and 75 kg, are at the center of a 60-m-diameter circular rink. The skaters push off against each other and glide to opposite edges of the rink. If the heavier...
A ball of mass m and another ball of mass 3m are placed inside a smooth metal tube with a massless spring compressed between them. When the spring is released, the heavier ball flies out of one end...
Two particles collide and bounce apart. FIGURE EX11.31 shows the initial momenta of both and the final momentum of particle 2. What is the final momentum of particle 1? Write your answer using unit...
An object at rest explodes into three fragments. FIGURE EX11.32 shows the momentum vectors of two of the fragments. What is the momentum of the third fragment? Write your answer using unit vectors....
A 20 g ball of clay traveling east at 3.0 m/s collides with a 30 g ball of clay traveling north at 2.0 m/s. What are the speed and the direction of the resulting 50 g ball of clay? Give your answer...
At the center of a 50-m-diameter circular ice rink, a 75 kg skater traveling north at 2.5 m/s collides with and holds on to a 60 kg skater who had been heading west at 3.5 m/s. a. How long will it...
A small rocket with 15 kN thrust burns 250 kg of fuel in 30 s. What is the exhaust speed of the hot gases?
A 2.0 kg object is moving to the right with a speed of 1.0 m/s when it experiences the force shown in FIGURE EX11.8. What are the objects speed and direction after the force ends? F, (N) 1.0 s - t...
A 250 g ball collides with a wall. FIGURE EX11.13 shows the balls velocity and the force exerted on the ball by the wall. What is v fx , the balls rebound velocity? F, (N) V, (m/s) 500 - VEr 8.0 ms...
A rocket in deep space has an exhaust-gas speed of 2000 m/s. When the rocket is fully loaded, the mass of the fuel is five times the mass of the empty rocket. What is the rockets speed when half the...
A tennis player swings her 1000 g racket with a speed of 10 m/s. She hits a 60 g tennis ball that was approaching her at a speed of 20 m/s. The ball rebounds at 40 m/s. a. How fast is her racket...
A 60 g tennis ball with an initial speed of 32 m/s hits a wall and rebounds with the same speed. FIGURE P11.39 shows the force of the wall on the ball during the collision. What is the value of F max...
A 500 g cart is released from rest 1.00 m from the bottom of a frictionless, 30.0° ramp. The cart rolls down the ramp and bounces off a rubber block at the bottom. FIGURE P11.40 shows the force...
A particle of mass m is at rest at t = 0. Its momentum for t > 0 is given by p x = 6t 2 kg m/s, where t is in s. Find an expression for F x (t), the force exerted on the particle as a function of...
A rocket in deep space has an empty mass of 150 kg and exhausts the hot gases of burned fuel at 2500 m/s. It is loaded with 600 kg of fuel, which it burns in 30 s. What is the rockets speed 10 s, 20...
A spaceship of mass 2.0 10 6 kg is cruising at a speed of 5.0 10 6 m/s when the antimatter reactor fails, blowing the ship into three pieces. One section, having a mass of 5.0 10 5 kg, is blown...
Is the center of mass of the dumbbell in FIGURE Q12.1 at point a, b, or c? Explain. a b FIGURE Q12.1
A high-speed drill reaches 2000 rpm in 0.50 s. a. What is the drills angular acceleration? b. Through how many revolutions does it turn during this first 0.50 s?
A ceiling fan with 80-cm-diameter blades is turning at 60 rpm. Suppose the fan coasts to a stop 25 s after being turned off. a. What is the speed of the tip of a blade 10 s after the fan is turned...
An 18-cm-long bicycle crank arm, with a pedal at one end, is attached to a 20-cm-diameter sprocket, the toothed disk around which the chain moves. A cyclist riding this bike increases her pedaling...
You have two solid steel spheres. Sphere 2 has twice the radius of sphere 1. By what factor does the moment of inertia I 2 of sphere 2 exceed the moment of inertia I 1 of sphere 1?
The three masses shown in Figure EX12.7 are connected by massless, rigid rods. What are the coordinates of the center of mass? B 300 g 10 cm 12 cm 100 g 200 g FIGURE EX12.7
Six forces are applied to the door in FIGURE Q12.8. Rank in order, from largest to smallest, the six torques Ï a to Ï f about the hinge on the left. Explain. F LI4 L/4 L/4 L/4 ' Td 2F T. ...
What is the rotational kinetic energy of the earth? Assume the earth is a uniform sphere. Data for the earth can be found inside the back cover of the book.
The three 200 g masses in Figure EX12.11 are connected by massless, rigid rods. a. What is the triangles moment of inertia about the axis through the center? b. What is the triangles kinetic energy...
The solid cylinder and cylindrical shell in FIGURE Q12.11 have the same mass, same radius, and turn on frictionless, horizontal axles. (The cylindrical shell has lightweight spokes connecting the...
The four masses shown in Figure EX12.13 are connected by massless, rigid rods. a. Find the coordinates of the center of mass. b. Find the moment of inertia about an axis that passes through mass A...
Is the angular momentum of disk a in FIGURE Q12.13 larger than, smaller than, or equal to the angular momentum of disk b? Explain. Ib = 2r, wn = 2w, b FIGURE Q12.13
In Figure EX12.18, what is the net torque about the axle? 30 N 4.0 cm 20 N
In Figure EX12.19, what magnitude force provides 5.0 N m net torque about the axle? 10 cm 10 cm
The 20-cm-diameter disk in Figure EX12.20 can rotate on an axle through its center. What is the net torque about the axle? y 30 N, 30 N 45 5.0 5.0 c cm 20 N 20 N FIGURE EX12.20
The three masses shown in Figure EX12.15 are connected by massless, rigid rods. a. Find the coordinates of the center of mass. b. Find the moment of inertia about an axis that passes through mass A...
An objects moment of inertia is 2.0 kg m 2 . Its angular velocity is increasing at the rate of 4.0 rad/s per second. What is the net torque on the object?
An object whose moment of inertia is 4.0 kg m 2 experiences the torque shown in Figure EX12.25. What is the objects angular velocity at t = 3.0 s? Assume it starts from rest. (Nm) 0+ -t (s) 3 FIGURE...
A 1.0 kg ball and a 2.0 kg ball are connected by a 1.0-m-long rigid, massless rod. The rod is rotating cw about its center of mass at 20 rpm. What net torque will bring the balls to a halt in 5.0 s?
Starting from rest, a 12-cm-diameter compact disk takes 3.0 s to reach its operating angular velocity of 2000 rpm. Assume that the angular acceleration is constant. The disks moment of inertia is 2.5...
A 4.0 kg, 36-cm-diameter metal disk, initially at rest, can rotate on an axle along its axis. A steady 5.0 N tangential force is applied to the edge of the disk. What is the disks angular velocity,...
The object shown in Figure EX12.30 is in equilibrium. What are the magnitudes of F 1 and F 2 ? 2.0 m 1.0 m f40 N Massless FIGURE EX12.30
The 3.0-m-long, 100 kg rigid beam of Figure EX12.31 is supported at each end. An 80 kg student stands 2.0 m from support 1. How much upward force does each support exert on the beam? 2.0 m 3.0 m...
A solid sphere of radius R is placed at a height of 30 cm on a 15 slope. It is released and rolls, without slipping, to the bottom. From what height should a circular hoop of radius R be released on...
Evaluate the cross products A Ã B and C Ã D. (a) A (b) 4 90 45 FIGURE EX12.38
Vector A = 3i + j and vector B = 3i - 2j + 2k. What is the cross product A B?
Force F = -10j N is exerted on a particle at r = (5i + 5j) m. What is the torque on the particle about the origin?
A 1.3 kg ball on the end of a lightweight rod is located at (x, y) = (3.0 m, 2.0 m), where the y-axis is vertical. The other end of the rod is attached to a pivot at (x, y) = (0 m, 3.0 m). What is...
What are the magnitude and direction of the angular momentum relative to the origin of the 200 g particle in FIGURE EX12.42? 200 g 45 2.0 m- 3.0 m/s - 1.0 m
What is the angular momentum vector of the 2.0 kg, 4.0-cm-diameter rotating disk in FIGURE EX12.43? y 600 rpm FIGURE EX12.43
What is the angular momentum vector of the 500 g rotating bar in FIGURE EX12.44? 120 rpm 2.0 m FIGURE EX12.44
How fast, in rpm, would a 5.0 kg, 22-cm-diameter bowling ball have to spin to have an angular momentum of 0.23 kg m 2 /s?
A 2.0 kg, 20-cm-diameter turntable rotates at 100 rpm on frictionless bearings. Two 500 g blocks fall from above, hit the turntable simultaneously at opposite ends of a diameter, and stick. What is...
A 75 g, 6.0-cm-diameter solid spherical top is spun at 1200 rpm on an axle that extends 1.0 cm past the edge of the sphere. The tip of the axle is placed on a support. What is the tops precession...
A 300 g ball and a 600 g ball are connected by a 40-cm-long massless, rigid rod. The structure rotates about its center of mass at 100 rpm. What is its rotational kinetic energy?
An 800 g steel plate has the shape of the isosceles triangle shown in FIGURE P12.50. What are the x- and y-coordinates of the center of mass? y 20 cm 30 cm FIGURE P12.50
Determine the moment of inertia about the axis of the object shown in FIGURE P12.51. Rod of p , mass M Rotation axis FIGURE P12.51
What is the moment of inertia of a 2.0 kg, 20-cm-diameter disk for rotation about an axis (a) Through the center, (b) Through the edge of the disk?
Calculate the moment of inertia of the rectangular plate in FIGURE P12.54 for rotation about a perpendicular axis through the center. Rotation axis L L FIGURE P12.54
a. A disk of mass M and radius R has a hole of radius r centered on the axis. Calculate the moment of inertia of the disk. b. Confirm that your answer agrees with Table 12.2 when r = 0 and when r =...
Consider a solid cone of radius R, height H, and mass M. The volume of a cone is 1/3HR 2 . a. What is the distance from the apex (the point) to the center of mass? b. What is the moment of inertia...
A persons center of mass is easily found by having the person lie on a reaction board. A horizontal, 2.5-m-long, 6.1 kg reaction board is supported only at the ends, with one end resting on a scale...