1. A boy pushes a 5.00 kg cart in a circle, starting at 0.500 m/s and accelerating to 3.00 m/s. How much work was done on the cart?
2. A 30.0 kg box sliding at 5.00 m/s on a rough surface is brought to rest by 20.0 N of friction. What distance does the box slide?
3. A 1000.0 kg truck accelerates from 20.0 m/s to 25.0 m/s over a distance of 300.0 m. What is the average net force on the truck?
4. A space ship of mass 5.00 ×104 kg is traveling at a speed 1.15 × 104 m/s in outer space. Except for the force generated by its own engine, no other force acts on the ship. As the engine exerts a constant force of 4.00 × 105 N, the ship moves a distance of 2.50 × 106 m in the direction of the force of the engine.
a. Determine the final speed of the ship using the work-energy theorem.
b. Determine the final speed of the ship using the kinematics equations.
5. A force of 6.0 N is used to accelerate a mass of 1.0 kg from rest for a distance of 12m. The force is applied along the direction of travel. The coefficient of kinetic friction is 0.30. What is the
a. work done by the applied force?
b. work done by friction?
c. kinetic energy at the 12-m mark?
6. A 0.600-kg particle has speed of 2.00 m/s at point A and kinetic energy of 7.50 J at point B. What is
a. its kinetic energy at A?
b. its speed at B?
c. the total work done on the particle as it moves from A to B?
7. Two carts, one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?
8. A weapon fired a 25.8-kg shell with a muzzle speed of 880 m/s. What propulsive force was necessary to attain the muzzle speed within the 6.00-m barrel? (Assume constant acceleration and neglect the Earth's gravitational effect.
9. A catcher stops a 91 mi/h pitch in his glove, bringing it to rest in 0.00179 m. If force exerted by the catcher is 785 N, what is the mass of the ball?
10. A baggage handler drops your 7.80 kg suitcase onto a conveyor belt running at 1.60 m/s. The materials are such that µs= 0.470 and µk = 0.150 . How far is your suitcase dragged before it is riding smoothly on the belt?
11. A 12.4 g bullet is fired horizontally into a 96 g wooden block initially at rest on a horizontal surface. After impact, the block slides 7.5 m before coming to rest. If the coefficient of kinetic friction between block and surface is 0.650, what was the speed of the bullet immediately before impact?
12. A toy cart moves with a kinetic energy of 30 J. If its speed is doubled, what will its kinetic energy be?
13. A car traveling 59 miles/hour locks up its brakes. The brakes are released when the car reaches 42 miles/hour. The mass of the car is 79.2 slugs. Calculate the Energy lost to Friction in Joules.
14. A 70 kg diver steps off a 10 m tower and drops from rest straight down into the water. If he comes to rest 5 m beneath the surface, determine the average resistive force exerted on him by the water.
15. The masses of the javelin, discus, and shot are 0.80 kg, 2.0 kg, and 7.2 kg, respectively, and record throws in the corresponding track events are about 98 m, 74 m, and 23 m, respectively. Neglecting air resistance, calculate the minimum initial kinetic energies that would produce these throws and estimate the average force exerted on each object during the throw, assuming the force acts over a distance of 2 m.
WORK and POTENTIAL ENERGY PROBLEMS
1. How much work is done by a crane lifting a 200.0 kg crate from the ground to a floor 21.0 m above the ground. What is the change in gravitational potential energy of the crate?
2. A 25-kg box slides, from rest, down a 9.0-m-long incline that makes an angle of 15° with the horizontal. The speed of the box when it reaches the bottom of the incline is 2.4 m/s.
a. What is the coefficient of kinetic friction between the box and the surface of the incline?
b. How much work is done on the box by the force of friction and
c. What is the change in the potential energy of the box?
3. A 40.0-kg wagon is towed up a hill inclined at 18.5º with respect to the horizontal. the tow rope is parallel to the incline and has a tension of 140N in it. Assume that the wagon starts from rest at the bottom of the hill, and neglect friction. How fast is the wagon going after moving 80 m up the hill?
4.A 25.6kg child pulls a 4.81kg toboggan up a hill inclined at 25.7° to the horizontal. The vertical height of the hill is 27.3 m. Friction is negligible. Determine how much work the child must do on the toboggan to pull it at a constant velocity up the hill.
5. An 81.0-kg in-line skater does +3500 J of nonconservative work by pushing against the ground with his skates. In addition, friction does -710 J of nonconservative work on the skater. The skater's initial and final speeds are 2.50 m/s and 1.60 m/s, respectively. (a) Has the skater gone uphill, downhill, or remained at the same level? (b) Calculate the change in height of the skater.
6. A solid object with mass (m) is initially at rest. The local gravitational field, causes a downward weight, mg. An applied vertical force (F) is constant for time (t), during which time the object undergoes constant acceleration (a), reaching upward speed (V), and total displacement (h). Use newton's second law to derive an expression (in terms of m,g,h,and V) for the work. Start from the definition of work, W=F*h. The solution cannot contain F or t (time).
2. How fast must a 10.5 g bullet be traveling when it strikes a ballistic pendulum that consists of a block of wood of mass 3.00 kg that is suspended by a cord. The bullet gets embedded in the block. The block rises by 0.220 m after the impact.
3. Jane, looking for Tarzan, is running at a top speed (5.3m/s) and grabs a vine hanging vertically from a tall tree in the jungle.
a. How high can she swing upward?
b. Does the length of vine affect the answer?
4. A roller coaster at the top of a 39.0 m high vertical loop is traveling 13.8 m/s. Find the speed of the cars as they move through the bottom of the loop.
5. Analyze the motion of a simple swinging pendulum in terms of energy, (a) ignoring friction; and (b) taking friction into account. Explain why a grandfather clock has to be wound up.
6. A ball is attached to a horizontal cord of length L whose other end is fixed.
a. If the ball is released, what will be its speed at the lowest point of its path?
b. A peg is located a distance h directly below the point of attachment of the cord. If h= 0.080L, what will be the speed of the ball when it reaches the top of the circular path about the peg?
7. A projectile is fired at an upward angle of 45.0 degree from the top of a 265 m cliff with a speed of 185 m/s. What will be its speed when it strikes the ground below?
8. If a projectile is launched from Earth with a speed equal to the escape speed, how high above the Earth's surface is it when its speed is one third the escape speed?
9. Two baseballs, each with a mass of 0.116 kg, are separated by a distance of 380 m in outer space, far from any other objects. If the balls are released from rest, what speed do they have when their separation has decreased to 171 m? Ignore the gravitational effects from any other objects.
10. A gymnast practices two dismounts form the high bar on the uneven parallel bars. During one dismount she swings up off the bar with an initial upward velocity of + 4.0 m/s. In the second, she releases form the same height but with and initial downward velocity of -3.0m/s. How do the final velocities of the gymnast as she reaches the ground differ? What is her acceleration in each case?
11. A 200 g ball is thrown upwards with an initial kinetic energy of 10 Joules. What maximum height will the ball attain? (neglect air resistance)
12. Bruce stands on a bank beside a pond, grasps the end of a 20.0 m long rope attached to a nearby tree and swings to drop into the water. if the rope starts at an angle 35 degrees with the vertical, what is Bruce's speed at the bottom of the swing?
13. Two circus performers, Jack and Jill, whose total mass is 120 kg, start a swing which is 5m long such that initially the rope attached to their swing makes an angle of 36 degrees with the horizontal. At the bottom of the arc, Jill, whose mass is 52 kg, steps off. What is the maximum height of a landing ramp that jack can reach as the swing continues?
14.
a. A 1.9-kg block slides down a curved, frictionless ramp. The top of the ramp is 1.5 m above ground; the bottom of the ramp is 0.25 m above the ground. The block leaves the ramp moving horizontally, and lands a horizontal distance D away. What is the distance D?
b. Suppose the ramp is not frictionless. Find the distance D for the case in which friction on the ramp does -9.7 J of work on the block before it becomes airborne.
15. In a tennis match, a player wins a point by hitting the ball sharply to the ground on the opponent's side of the net. (a) If the ball bounces upward from the ground with a speed of 16 m/s and is caught by a fan with a speed of 12 m/s, how high above the court is the fan? Ignore air resistance.
16. From what height would a car have to be dropped to have the same kinetic energy that it has when being driven at 100 km/h?
17. A 135 m long ramp is to be built for a ski jump. If a skier starting from rest at the top is to have a speed no faster than 19m/s at the bottom, what should be the maximum angle of inclination?
18. Show that the escape speed from the surface of a planet of uniform density is directly proportional to the radius of the planet.
19. Two objects, m1 = 4.50kg and m2 = 3.00kg, are connected by a light string passing over a light frictionless pulley. The object of the mass 4.50kg is released from rest 4.50m above the ground. Using the principle of conservation of energy, determine the speed of the 3.00kg object just as the 4.50kg object hits the ground.
20.
(a) What is the escape speed on a spherical asteroid whose radius is 525km and whose gravitational acceleration at the surface is 2.7m/s2? (in m/s)
(b.)How far from the surface will a particle go if it leaves the asteroids
surface with a radial speed of 1000m/s? (in m)
(c.) With what speed will an object hit the asteroid if it is dropped from
1000km above the surface? (in m/s)
21. In the looping the loop setup, an object of mass m is released from rest from A with the initial height h and loops the loop in the circular track of radius R.
a)Express the initial mechanical energy at A in terms of m, g, h
b) Express the energy at point B at the top of the vertical circle in terms of mass m, velocity v, radius R and g
c) If in the absence of friction the object just manages to loop the loop without losing contact with the track, what is the minimum height h from which you will need to release the object? Express your answer in terms of R .
22. A 75 kg man steps out a window and falls (from rest) 1 m to a sidewalk.
a. What is the speed just before his feet strike the pavement?
b. If the man falls with his knees and ankles locked, the only cushion for his fall is an approximately 0.50 cm give in the pads of his feet. Calculate the average force exerted on him by the ground in this situation.
B. Kinetic Energy / Elastic Potential Energy
1. A 0.150 kg puck on a frictionless surface is pressed against a spring with a spring constant of 2.00 N/m. The pressure causes the spring to compress 0.30 m. What velocity will the puck attain when released?
2. A 200 g mass is attached to a spring of spring constant k. The spring is compressed 20 cm from its equilibrium value. When released the mass reaches a speed of 5 m/s. What is the spring constant (in N/m)?
3. A 1200-kg car rolling on a horizontal surface has a speed v= 65km/h when it strikes a horizontal coiled spring and is brought to rest in a distance of 2.2 m. What is the spring stiffness constant of the spring?
4. A 0.444 kg mass is attached to a spring with a force constant of 26.8 N/m on a frictionless horizontal surface and released from rest a distance of 3.15 cm from the equilibrium position of the spring. What is the speed of the mass when it is halfway to the equilibrium position?
5. A 34-g bullet traveling at 120m/s embeds itself in a wooden block on a smooth surface. The block then slides toward spring and collides with it. The block compresses the spring(k=99 N/m)a maximum of 1.2 cm. Calculate the mass of the block of wood.
6. An archer is taking aim at a target that is exactly 20 m away in the horizontal direction (the target is at the same height above the ground that the arrow starts from). The mass of the arrow is 132 g. If the spring constant for the bowstring is 1500 N/m and the string is stretched 82 cm from its equilibrium, find the angle above horizontal that the arrow must be fired at to hit the target.
7. A cannon of m1=800kg (when unloaded) initially resting on a frictionless surface is loaded with a "shot" of mass m2=10kg. The cannon is aimed at mass m3=7990kg, which is connected to a massless spring of force constant k=4500N/m. The cannon is fired and the shot inelastically collides with Mass m3 and sticks in it. The combined system compresses the spring a maximum distance of d=.500m. a) Determine the speed of m2 just before it collides with m3(You may assume that m2 travels in a straight line. b) Determine the recoil speed of the cannon.
2. A 1000 kg car accidentally drops from a crane and crashes at 30 m/s to the ground below and comes to an abrupt halt. What impulse acts on the car when it crashes?
3. If a force of 300N is exerted upon a 60 kg mass for 4 seconds, how much impulse does the mass experience?
4. Two pucks with identical mass are traveling on a frictionless surface at right angles to each other with velocities v1 and v2 respectively (v1 = 2v2). The pucks collide and stick together.
a. Draw momentum vectors for both pucks before the collision.
b. Draw the momentum vector for the combined body immediately after the collision.
c. What is the impulse of the system?
5. A billiard ball approaches a cushioned edge of a billiard table with momentum, p. After the collision with the cushion, it bounces straight back with the same amount of momentum in the opposite direction. What is the impulse on the ball?
6. A bullet, of mass 20 g, traveling at 350 m/s, strikes a steel plate at an angle of 30-degrees with a plane of the plate. It ricochets off at the same angle, at a speed of 320 m/s. What is the magnitude of the impulse that the wall gives to the bullet?
7. A bungee jumper (m = 77.00 kg) tied to a 32.00 m cord, leaps off a 62.00 m tall bridge. He falls to 9.00 m above the water before the bungee cord pulls him back up. What size impulse is exerted on the bungee jumper while the cord stretches.
8. While waiting in his car at a stoplight, an 80-kg man and his car are suddenly accelerated to a speed of 5 m/s as a result of a rear-end collision. Assuming the time taken to be 0.3s, find the
a) impulse on the man and
b) the average force exerted on him by the back seat of his car
9. The momentum of a 30.0-g sparrow with a speed of 12 m/s is 0.36 kg*m/s. What will be its momentum 12s later if a constant .02 N force due to air resistance acts on it?
10. Two carts one twice the mass of the other, experience the same force for the same time. What is their difference in momentum? What is their difference in kinetic energy?
11. During the service of a professional tennis player the racket exerted an average force of 152.0 N on the ball. If the ball has a mass of 0.070 kg and was in contact with the strings of the racket for 0.030 s, what was the kinetic energy of the ball as it left the racket? Assume that the ball started from rest. Assume that air resistance was negligible.
1. A girl, mass 70.0 kg, is running 3.0 m/s east when she jumps onto a stationary skateboard, mass 2.0 kg. What is the velocity of the girl and skateboard assuming they move off together?
2. In a football game, a receiver is standing still, having just caught a pass. Before he can move, a tackler from the opposing team, running at 5.0 m/s, grabs him and holds onto him, and the two move off together with a velocity of 2.7 m/s in the same direction in which the tackler was running. If the mass of the tackler is 100 kg, what is the mass of the receiver?
3. A 1 kg glider and a 3 kg glider both slide toward each other at 1 m/s on an air track. They collide and stick. what will be the speed of the combined mass?
4. A bullet of mass, "m," is being fired with a velocity, "v," into a block of mass, "M." Find the loss in kinetic energy of the system.
5. A 6.00 g bullet is fired horizontally into a 1.50 kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.30. The bullet remains embedded in the block, which is observed to slide 0.25 m along the surface before stopping. What was the initial speed of the bullet?
6. A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.914 kg that rests on a frictionless, horizontal surface and is attached to a coil spring (Fig. 8.39). The impact compresses the spring 15.0 cm. Calibration of the spring shows that a force of 0.750 N is required to compress the spring 0.230 cm.
(a) Find the magnitude of the block's velocity just after impact.
(b) What was the initial speed of the bullet?
7. A 1500 Kg space probe is orbiting the Earth at a distance of 25000 Km from the Earth's center. The probe is hit head on by a 1000 kg meteor moving at 1000 kph. After the completely inelastic collision, will the meteorite and crumpled probe will fall together into a lower orbit? Find the radius of a new stable orbit for this wreckage.
8. a. Find the speed at which Superman (mass=76.0 kg) must fly into a train (mass = 19537 kg) traveling at 65.0 km/hr to stop it.
b. Calculate the time Superman must take to stop the train, if the passengers experience an average horizontal force of 0.550 their own weight.
B. Collisions without Coupling
1. A steel ball bearing, with mass 20.0 g, is rolling along a level tabletop at 0.50 m/s. A glass marble, with mass 5.00 g, rolls headlong toward the ball bearing at 0.75 m/s. Immediately after the collision, the ball bearing continues in its original direction at 0.10 m/s. What is the velocity of the marble?
2. A 1kg ball moving at a speed of 10 m/s in the positive x direction collides head on with a 2 kg ball at rest. The velocities of the 1kg and 2 kg ball after the collision are respectively?
3. An 74.5 kg object moving to the right at 34.3 cm/sec overtakes and collides elastically with a second 55.8 kg object moving in the same direction at 16.7 cm/s. Find the velocity of the second object after the collision. Answer in cm/s.
4. In an inelastic collision, is the final total momentum more,less, or the same as the initial momentum?
5. A 1700 kg car is moving westward with a speed of 21 m/s, and a 3400 kg truck is traveling east with a speed of 14 m/s. Find the velocity of the center of mass of the system. (Take east to be the positive x direction.)
6. A ball of 0.4-kg mass and a speed of 3 m/s has a head on collision with a 0.6-kg mass initially at rest. find The speed of the 0.4-kg mass if the speed of the 0.6-kg mass after the collision is 2.4 m/s. Is this collision an elastic collision or an inelastic collision?
7. At one instant, the center of mass of a system of two particles is located on the x axis at x = 5.0 m and has a velocity of (6.0 m/s). One of the particles is at the origin. The other particle has a mass of 0.30 kg and is at rest on the x axis at x = 8.0 m.
(a) What is the mass of the particle at the origin?
(b) Calculate the total momentum of this system.
(c) What is the velocity of the particle at the origin?
8. Canadian nuclear reactors use heavy water moderators in which elastic collisions occur between the neutrons and deuterons of mass 2.0 u.
(a) What is the speed of a neutron, expressed as a fraction of its original speed, after a head-on, elastic collision with a deuteron which is initially at rest?
(b) What is its kinetic energy, expressed as a fraction of its original kinetic energy?
(c) How many such successive collisions will reduce the speed of a neutron to 1/27 of its original value?
C. Explosions
1. A boy, mass 70.0 kg, riding a skateboard, mass 2.0 kg, is traveling 3.0 m/s east when he attempts to jump forward from his skateboard. If his velocity immediately after leaving the skateboard is 3.1 m/s [E], what is the velocity of t he skateboard?
2. A 232 Th (thorium) nucleus at rest decays to a 228 Ra (radon) nucleus with the emission of an alpha particle. The total kinetic energy of the decay fragments is 6.54 x 10^-3 J. An alpha particle has 1.76% of the mass of a 228 Ra nucleus.
a) Calculate the kinetic energy of the recoiling 228 Ra nucleus.
b) Calculate the kinetic energy of the alpha particle.
3. A child in a boat throws a 6.4 kg package out horizontally with a speed of 10 m/s. Calculate the velocity of the boat immediately after, assuming it was initially at rest. The mass of the child is 26 kg and that of the boat is 45 kg.
4. A 30.5 kg girl is standing on a 90 kg plank. The plank is at rest on a flat frictionless ice surface. When the girl walks on the plank at a constant 2.17 m/s to right relative to plank, what is her velocity relative to the ice surface? Answer m/s.
5. A 13.8 kg block and a 25.3 kg block are resting on a horizontal frictionless surface. Between the two is squeezed a spring (spring constant = 1620 N/m). The spring is compressed by 0.143 m from it unstrained length. With what speed does each block move away when the mechanism keeping the spring squeezed is released?
6. A 11.9 kg gun at rest contains a 0.0018 kg bullet. When fired, the bullet leaves the gun with a forward velocity of 290 m/s. What is the recoil velocity of the gun in m/s?
7. A rocket launched in space (microgravity) acquires a final speed of 15.00 m/s. The initial mass is 450.0 g and the empty mass is 35.0 g. What is the exhaust velocity of the propellant?
D. Other
1. Two people, one of mass 72.8kg and the other of mass 52.4kg, sit in a rowboat of mass 81.6 kg. With the boat initially at rest, the two people, who have been sitting at opposite ends of the boat, 3.14m apart from each other, exchange seats. How far will the boat move?
G = 6.67 x 10-11 Nm2/kg2
1. A mass of 20.0 kg is located 4.0 m to the right of a mass of 30.0 kg.
a. What is the force on the 20.0 kg mass?
b. What is the force on the 30.0 kg mass?
2. A spaceship is traveling along a line connecting the centers of the Earth and the Moon. At what distance from the earth does the spaceship find the gravitational pull of the Earth equal in magnitude to that of the moon (as a percentage of the distance between the centers of the 2 bodies)?
3. Find the altitude above the Earth's surface where Earth's gravitational field strength would be two-thirds of its value at the surface.
4.Four masses form the vertices of a 1 m X 1 m square as shown. What is the gravitational force on the 3 kg mass due to the other three masses?
5. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?
6. The gravitational field intensity at the surface of a planet is 3.4N/kg. If a planet's mass is 7.2*1022 kg, what is its radius?
7. Suppose that material ejected from a volcano on Io reaches a height of 5.08 km after being projected straight upward with an initial speed of 127 m/s. Given that the radius of Io is 1820 km, calculate Io's mass.
8. A neutron star might have as much as five times the mass of our sun packed into a sphere about 10 km in radius! Estimate the surface gravity on this monster.
9. If the mass of Titan is 1.35*1023 kg and it's radius is 2570 km determine
a. the force at the surface on a 500 kg probe.
b. the acceleration due to titans mass.
10. What force does Earth exert on a 80.0kg astronaut at an altitude equivalent to 2.5 times Earth's radius?
11. What is the acceleration due to gravity at an altitude of 2*106 m above the earth\'s surface? Earth's mass is 5.98*1024 kg and of Earth's radius is 6.37*106 m .
12. A 492kg uniform solid sphere has a radius of .405m. Find the magnitude of the gravitational force (in N) exerted by the sphere on a 50.4g particle located 0.197m from the center of the sphere?
13. A hypothetical planet has a radius 2.0 times that of Earth, but has the same mass. What is the acceleration due to gravity near its surface?
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