Chapter 8
The initial and final momenta of an object are shown below. Which green arrow best indicates the direction of the net impulse applied to the object?
D. 4
Block A on the left has mass 1.00 kg. Block B on the right has mass 3.00 kg. Block A is initially moving to the right at 6.00 m/s, while block B is initially at rest. The surface they move on is level and frictionless. What is the velocity of the center of mass of the two blocks after the blocks collide?
C. 1.50 m/s, to the right.
Block A on the left has mass 1.00 kg. Block B on the right has mass 3.00 kg. Block A is initially moving to the right at 6.00 m/s, while block B is initially at rest. The surface they move on is level and frictionless. What is the velocity of the center of mass of the two blocks before the blocks collide?
C. 1.50 m/s, to the right.
A 3.00-kg rifle fires a 0.00500-kg bullet at a speed of 300 m/s. Which force is greater in magnitude: the force that the rifle exerts on the bullet or the force that the bullet exerts on the rifle?
C. Both forces have the same magnitude.
You are testing a new car using crash test dummies. Consider two ways to slow the car from 90 km/h (56 mi/h) to a complete stop: (i) You let the car slam into a wall, bringing it to a sudden stop. (ii) You let the car plow into a giant tub of gelatin so that it comes to a gradual halt. In which case is there a greater impulse of the net force on the car?
C. The impulse is the same in both cases.
You are standing on a skateboard, initially at rest. A friend throws a very heavy ball towards you. You can either catch the object or deflect the object back towards your friend (such that it moves away from you with the same speed as it was originally thrown). What should you do in order to MINIMIZE your speed on the skateboard?
Catch the ball.
Two objects with different masses collide with and bounce off each other. Compared to before the collision, the system of two objects after the collision has
E. Not enough information is given to decide.
What represents the impulse of the force in a graph of force versus time?
The impulse is equal to the area under the curve.
A shell explodes into two fragments, one fragment 25 times heavier than the other. If any gas from the explosion has negligible mass, then
The momentum change of the lighter fragment is exactly the same as the momentum change of the heavier fragment.
A red ball with a velocity of +3.0 m/s collides head-on with a yellow ball of equal mass moving with a velocity of −2.0 m/s. What is the velocity of the two balls after the elastic collision?
The velocity of the red ball is −2.0 m/s; the velocity of the yellow ball is +3.0 m/s.
James (mass 85.0 kg) and Ramon (mass 69.0 kg) are 20.0 m apart on a frozen pond. Midway between them is a mug of their favorite beverage. They pull on the ends of a light rope stretched between them. Ramon pulls on the rope to give himself a speed of 1.10 m/s. What is James's speed? Express your answer with the appropriate units.
VJ = 0.893 m/s
Archerfish are tropical fish that hunt by shooting drops of water from their mouths at insects above the water's surface to knock them into the water, where the fish can eat them. A 65 g fish at rest just at the surface of the water can expel a 0.30 g drop of water in a short burst of 5.0 ms. High-speed measurements show that the water has a speed of 2.5 m/s just after the archerfish expels it. What is the speed of the archerfish immediately after it expels the drop of water?
0.012 m/s
Two ice skaters push off against one another starting from a stationary position. The 45.0-kg skater acquires a speed of 0.375 m/s. What speed does the 60.0-kg skater acquire? Assume that any other unbalanced forces during the collision are negligible.
0.281 m/s
Two objects of the same mass move along the same line in opposite directions. The first mass is moving with speed v. The objects collide, stick together, and move with speed 0.100v in the direction of the velocity of the first mass before the collision. What was the speed of the second mass before the collision?
0.800 v
Question 11:A billiard ball traveling at 3.00 m/s collides perfectly elastically with an identical billiard ball initially at rest on the level table. The initially moving billiard ball deflects 30.0° from its original direction. What is the speed of the initially stationary billiard ball after the collision?
1.50 m/s
During a collision with a wall, the velocity of a 0.200-kg ball changes from 20.0 m/s toward the wall to 12.0 m/s away from the wall. If the time the ball was in contact with the wall was 60.0 ms, what was the magnitude of the average force applied to the ball?
107 N
A 0.500-kg ball traveling horizontally on a frictionless surface approaches a very massive stone at 20.0 m/s perpendicular to wall and rebounds with 70.0% of its initial kinetic energy. What is the magnitude of the change in momentum of the stone?
18.4 kg * m/s
A firecracker breaks up into several pieces, one of which has a mass of 200 g and flies off along the x-axis with a speed of 82.0 m/s. A second piece has a mass of 300 g and flies off along the y-axis with a speed of 45.0 m/s. What are the magnitude and direction of the total momentum of these two pieces?
21.2 kg ⋅ m/s at 39.5° from the x-axis
A plate falls vertically to the floor and breaks up into three pieces, which slide along the floor. Immediately after the impact, a 320-g piece moves along the x-axis with a speed of 2.00 m/s and a 355-g piece moves along the y-axis with a speed of 1.50 m/s. The third piece has a mass of 100 g. In what direction does the third piece move? You can neglect any horizontal forces during the crash.
219.8 degrees from the x-axis
A 2.00-m rod of negligible mass connects two very small objects at its ends. The mass of one object is 1.00 kg and the mass of the other is unknown. The center of mass of this system is on the rod a distance 1.60 m from the 1.00-kg mass object. What is the mass of the other object?
4.00 kg
A basketball falling straight down bounces on the floor and rebounds straight up. Which green arrow best indicates the direction of the net impulse applied to the ball by the floor?
A. 1
A ball (mass 0.40 kg) is initially moving to the left at 30 m/s. After hitting the wall, the ball is moving to the right at 20 m/s. What is the impulse of the net force on the ball during its collision with the wall?
A. 20 kg * m/s to the right
A 310-g air track cart is traveling at 1.25 m/s and a 260-g cart traveling in the opposite direction at 1.33 m/s. What is the speed of the center of mass of the two carts?
0.0732 m/s
Two objects with different masses collide with and stick to each other. Compared to before the collision, the system of two objects after the collision has
B. The same amount of total momentum but less total kinetic energy.
A small rocket burns a mass 0.0500 kg of fuel per second, ejecting it as a gas with a velocity relative to the rocket of magnitude 1590 m/s. What is the thrust of the rocket? Express your answer in newtons.
F = 79.5 N
On a smooth horizontal floor, an object slides into a spring which is attached to another mass that is initially stationary. When the spring is most compressed, both objects are moving at the same speed. Ignoring friction, what is conserved during this interaction?
Momentum and mechanical energy
For an elastic collision, which of the following statements are true? Choose all that apply. Momentum is conserved. Momentum is gained. Kinetic energy is gained. Kinetic energy is lost. Momentum is lost. Kinetic energy is conserved.
Momentum is conserved. Kinetic energy is conserved.
For an INELASTIC collision, which of the following statements are true? Choose all that apply. Momentum is conserved. Kinetic energy is gained. Momentum is gained. Momentum is lost. Kinetic energy is lost. Kinetic energy is conserved.
Momentum is conserved. Kinetic energy is lost.
Consider two less-than-desirable options. In the first you are driving 30 mph and crash head-on into an identical car also going 30 mph. In the second option you are driving 30 mph and crash head-on into a stationary brick wall. In neither case does your car bounce off the thing it hits, and the collision time is the same in both cases. Which of these two situations would result in the greatest impact force?
The force would be the same in both cases.
In a lab environment, you are investigating the impulse of a force exerted on a brick when the brick's speed is reduced from 2.5 m/s to a complete stop. First, you allow the brick to slam into a secured piece of wood, bringing the brick to a sudden stop. Second, you allow the brick to plow into a large slab of gelatin so that the brick comes to a gradual halt. In which situation is there a greater impulse of the force on the brick?
The impulse is the same in both situations.
A 1.0-kg block and a 2.0-kg block are pressed together on a horizontal frictionless surface with a compressed very light spring between them. They are not attached to the spring. After they are released and have both moved free of the spring
The lighter block will have more kinetic energy than the heavier block.
In an INELASTIC collision between two objects
The momentum of the system is conserved but the kinetic energy of the system is not conserved.
A freight car moves along a frictionless level railroad track at constant speed. The freight car is open on the top. A large load of sand is suddenly dumped into the freight car. What happens to the speed of the freight car?
The speed of the freight car decreases.
When a person steps forward out of a small boat onto a dock, the boat recoils backward in the water. Why does this occur?
The total momentum of the system is conserved.
A packing crate with mass 80.0 kg is at rest on a horizontal, frictionless surface. At t = 0 a net horizontal force in the +x-direction is applied to the crate. The force has a constant value of 80.0 N for 12.0 s and then decreases linearly with time so it becomes zero after an additional 6.00 s. What is the final speed of the crate, 18.0 s after the force was first applied? Express your answer with the appropriate units.
v = 15.0 m/s
A 7.00 g bullet is fired horizontally into a 1.20 kg wooden block resting on a horizontal surface. The coefficient of kinetic friction between block and surface is 0.20. The bullet remains embedded in the block, which is observed to slide 0.390 m along the surface before stopping. What was the initial speed of the bullet? Express your answer with the appropriate units.
v = 210 m/s
A railroad handcar is moving along straight, frictionless tracks with negligible air resistance. In the following cases, the car initially has a total mass (car and contents) of 160 kg and is traveling east with a velocity of magnitude 4.60 m/s. Find the final velocity of the car in each case, assuming that the handcar does not leave the tracks. An object with a mass of 30.0 kg is thrown sideways out of the car with a speed of 2.50 m/s relative to the car's initial velocity. Express your answer with the appropriate units. An object with a mass of 30.0 kg is thrown backward out of the car with a velocity of 4.60 m/s relative to the initial motion of the car. Express your answer with the appropriate units. An object with a mass of 30.0 kg is thrown into the car with a velocity of 6.50 m/s relative to the ground and opposite in direction to the initial velocity of the car. Express your answer with the appropriate units.
v = 4.60 m/s east v = 5.66 m/s east v = 2.8 m/s east
Three objects A, B, and C are moving as shown in the figure below (Figure 1). Assume that vA = 10.8 m/s, vB = 10.0 m/s, and vC = 4.0 m/s. Find the x-component of the net momentum of the particles if we define the system to consist of A and C. Express your answer in kilogram meters per second. Find the y-component of the net momentum of the particles if we define the system to consist of A and C. Express your answer in kilogram meters per second. Find the x-component of the net momentum of the particles if we define the system to consist of B and C. Express your answer in kilogram meters per second. Find the y-component of the net momentum of the particles if we define the system to consist of B and C. Express your answer in kilogram meters per second. Find the x-component of the net momentum of the particles if we define the system to consist of all three objects. Express your answer in kilogram meters per second. Find the y-component of the net momentum of the particles if we define the system to consist of all three objects. Express your answer in kilogram meters per second.
Px = -40 kg*m/s Py = -54 kg*m/s Px = -10 kg*m/s Py = 52 kg*m/s Px = -10 kg*m/s
A lump of putty and a rubber ball have equal mass. Both are thrown with equal speed against a wall. The putty sticks to the wall. The ball bounces back at nearly the same speed with which it hit the wall. Which object experiences the greater momentum change?
The ball experiences the greater momentum change.
When a constant force acts on an object, what does the object's change in momentum depend upon? Check all that apply. The change in momentum depends upon the time interval during which the force acts. The change in momentum depends upon the change in the velocity of the object. The change in momentum depends upon the change in the position of the object. The change in momentum depends upon the magnitude of the force. The change in momentum depends upon the mass of the object.
The change in momentum depends upon the time interval during which the force acts. The change in momentum depends upon the change in the velocity of the object. The change in momentum depends upon the magnitude of the force. The change in momentum depends upon the mass of the object.
Jacques and George meet in the middle of a lake while paddling in their canoes. They come to a complete stop and talk for a while. When they are ready to leave, Jacques pushes George's canoe with a force →F→ to separate the two canoes. What is correct to say about the final momentum and kinetic energy of the system if we can neglect any resistance due to the water?
The final momentum is in the direction opposite of →F→ but the final kinetic energy is zero.
Which of the following statements are true? Select all correct responses. Choose all that apply. The vector sum of forces acting on a particle equals the rate of change of velocity of the particle with respect to time. The vector sum of forces acting on a particle equals the rate of change of momentum of the particle with respect to time. The total momentum of an isolated system is constant. The total momentum of any number of particles is equal to the vector sum of the momenta of the individual particles. The total momentum of any number of particles is equal to the algebraic sum of the momenta of the individual particles. The total momentum of any system is constant.
The vector sum of forces acting on a particle equals the rate of change of momentum of the particle with respect to time. The total momentum of an isolated system is constant. The total momentum of any number of particles is equal to the vector sum of the momenta of the individual particles.
Two asteroids of equal mass in the asteroid belt between Mars and Jupiter collide with a glancing blow. Asteroid A, which was initially traveling at vA1 = 40.0 m/s with respect to an inertial frame in which asteroid B was at rest, is deflected 30.0∘ from its original direction, while asteroid B travels at 45.0∘ to the original direction of A, as shown in (Figure 1). Find the speed of asteroid A after the collision. Express your answer in meters per second. Find the speed of asteroid B after the collision. Express your answer in meters per second. What fraction of the original kinetic energy of asteroid A dissipates during this collision?
VA2 = 29.3 m/s VB2 = 20.7 m/s Kdiss/origin = 0.196
A rifle bullet with mass 8.00 g strikes and embeds itself in a block with mass 0.992 kg that rests on a frictionless, horizontal surface and is attached to an ideal spring. 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 0.250 cm. (Figure 1) Find the magnitude of the block's velocity just after impact. Express your answer with the appropriate units. What was the initial speed of the bullet? Express your answer with the appropriate units.
Vblock = 2.60 m/s Vbullet = 325 m/s
In your job in a police lab, you must design an apparatus to measure the muzzle velocities of bullets fired from handguns. Your solution is to attach a 2.00 kg wood block that rests on a horizontal surface to a light horizontal spring. The other end of the spring is attached to a wall. Initially the spring is at its equilibrium length. A bullet is fired horizontally into the block and remains embedded in it. After the bullet strikes the block, the block compresses the spring a maximum distance d. You have measured that the coefficient of kinetic friction between the block and the horizontal surface is 0.38. The table below lists some firearms that you will test. A grain is a unit of mass equal to 64.80 mg. Bullet ID Type Bullet Mass (grains) Muzzle Velocity (ft/s) A .38 Spec Glaser Blue 80 1667 B .38 Spec Federal 125 945 C .44 Spec Remington 240 851 D .44 Spec Winchester 200 819 E .45 ACP Glaser Blue 140 1355 Of bullets A through E, which will produce the maximum compression of the spring? Of bullets A through E, which will produce the minimum compression of the spring? You want the maximum compression of the spring to be 0.31 m. What must be the force constant of the spring? Express your answer with the appropriate units. For the bullet that produces the minimum spring compression, what is the compression d if the spring has the force constant calculated in part C? Express your answer with the appropriate units.
bullet C bullet B k = 36 N/m d = 0.14 m
