1.
When comparing the momentum of two moving objects, which of the following is correct?
Correct Answer
C. The less massive object will have less momentum if the velocities are the same.
Explanation
The momentum of an object is directly proportional to its mass and velocity. In this case, the question states that the velocities are the same. According to the equation p = mv (momentum = mass x velocity), if the velocities are the same, the momentum will be determined by the mass. Therefore, the less massive object will have less momentum compared to the more massive object if their velocities are the same.
2.
Two skaters stand facing each other. One skater’s mass is 60 kg, and the other’s mass is 72 kg. If the skaters push away from each other without spinning,
Correct Answer
B. Their momenta are equal but opposite.
Explanation
When two skaters push away from each other without spinning, the total momentum of the system is conserved. Momentum is a vector quantity, meaning it has both magnitude and direction. Since the skaters are pushing away from each other, their momenta will have equal magnitudes but opposite directions. This means that their momenta are equal in magnitude but have opposite signs, resulting in their momenta being equal but opposite.
3.
In a two-body collision,
Correct Answer
A. Momentum is always conserved.
Explanation
In a two-body collision, momentum is always conserved. This means that the total momentum before the collision is equal to the total momentum after the collision. Even though kinetic energy may not be conserved in a collision, momentum is always conserved because it is a fundamental principle of physics.
4.
A person sitting in a chair with wheels stands up, causing the chair to roll backward across the floor. The momentum of the chair
Correct Answer
A. Was zero while stationary and increased when the person stood.
Explanation
When the person was sitting in the chair with wheels, the chair was stationary and had zero momentum. However, when the person stood up, they exerted a force on the chair in the forward direction, causing the chair to roll backward across the floor. This increase in motion indicates an increase in momentum. Therefore, the momentum of the chair was zero while stationary and increased when the person stood.
5.
Two swimmers relax close together on air mattresses in a pool. One swimmer’s mass is 48 kg, and the other’s mass is 55 kg. If the swimmers push away from each other,
Correct Answer
B. Their momenta are equal but opposite.
Explanation
When the swimmers push away from each other, according to the law of conservation of momentum, the total momentum of the system remains constant. Since momentum is a vector quantity, it has both magnitude and direction. The fact that the swimmers have equal but opposite momenta means that their magnitudes are the same, but they are moving in opposite directions. This ensures that the total momentum of the system remains unchanged.
6.
A 75 kg person walking around a corner bumped into an 80 kg person who was running around the same corner. The momentum of the 80 kg person
Correct Answer
C. Decreased.
Explanation
When the 75 kg person bumped into the 80 kg person, a collision occurred. According to the principle of conservation of momentum, the total momentum before and after the collision should be the same. Since the 75 kg person was walking and the 80 kg person was running, the 80 kg person had a higher initial momentum. As a result of the collision, some of the momentum of the 80 kg person would be transferred to the 75 kg person. Therefore, the momentum of the 80 kg person would decrease.
7.
The law of conservation of momentum states that
Correct Answer
D. The total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects.
Explanation
The law of conservation of momentum states that the total momentum of all objects interacting with one another remains constant regardless of the nature of the forces between the objects. This means that in a closed system, the total momentum before an interaction is equal to the total momentum after the interaction. This principle is based on the fact that momentum is a conserved quantity, meaning it cannot be created or destroyed, only transferred or redistributed among objects. Therefore, regardless of the forces involved, the total momentum of the system will always remain constant.
8.
When two ice skaters initially at rest push off one another, their final momenta are
Correct Answer
B. Equal in magnitude and opposite in direction.
Explanation
When two ice skaters initially at rest push off one another, their final momenta are equal in magnitude and opposite in direction. This is because of the law of conservation of momentum, which states that the total momentum of a system remains constant if no external forces act on it. Since the initial momentum of the system is zero, the final momentum must also be zero. Therefore, the skaters' momenta must cancel each other out, resulting in equal magnitudes but opposite directions.
9.
When two objects interact in an isolated system,
Correct Answer
D. The total momentum is always conserved.
Explanation
When two objects interact in an isolated system, the total momentum is always conserved. This means that the total momentum before the interaction is equal to the total momentum after the interaction. It does not matter if the objects are moving in the same or opposite directions, the total momentum of the system remains constant. This is a fundamental principle in physics known as the law of conservation of momentum.
10.
Conservation of momentum follows from
Correct Answer
C. Newton’s third law.
Explanation
Conservation of momentum follows from Newton's third law. Newton's third law states that for every action, there is an equal and opposite reaction. When two objects interact, the forces they exert on each other are equal in magnitude and opposite in direction. This means that the momentum lost by one object is gained by the other, resulting in the conservation of momentum. Therefore, Newton's third law is the correct answer as it directly relates to the principle of conservation of momentum.
11.
A 6.0 x 10^{-}^{2} kg tennis ball moves at a velocity of 12 m/s. The ball is struck by a racket, causing it to rebound in the opposite direction at a speed of 18 m/s. What is the change in the ball’s momentum?
Correct Answer
A. 0.36 kg*m/s
Explanation
When the tennis ball is struck by the racket, it experiences a change in velocity from 12 m/s in one direction to 18 m/s in the opposite direction. The change in velocity is calculated by subtracting the initial velocity from the final velocity, which in this case is 18 m/s - (-12 m/s) = 30 m/s. The momentum of an object is given by the product of its mass and velocity. Therefore, the change in momentum is equal to the change in velocity multiplied by the mass of the ball. The mass of the ball is given as 6.0 x 10^-2 kg. Multiplying the mass by the change in velocity, we get (6.0 x 10^-2 kg) * (30 m/s) = 0.36 kg*m/s.
12.
A student stumbles backward off a dock and lands in a small boat. The student isn't hurt, but the boat drifts away from the dock with a velocity of 0.85 m/s to the west. If the boat and student each have a mass of 68 kg, what is the student’s initial horizontal velocity?
Correct Answer
C. 0.85 m/s
Explanation
The student's initial horizontal velocity is 0.85 m/s because it is stated in the question that the boat drifts away from the dock with a velocity of 0.85 m/s to the west. Since the student is in the boat, their initial horizontal velocity would be the same as the boat's velocity.
13.
A 20.0 kg cannonball is fired from a 2.40 x 10^{3} kg. If the cannon recoils with a velocity of 3.5 m/s backwards, what is the velocity of the cannonball?
Correct Answer
A. 420 m/s
Explanation
When a cannonball is fired, according to Newton's third law of motion, there is an equal and opposite reaction. This means that the cannon will experience a recoil in the opposite direction to the cannonball. The momentum of the cannonball is equal to the momentum of the cannon.
To find the velocity of the cannonball, we can use the principle of conservation of momentum. The initial momentum of the system (cannonball + cannon) is zero since they were at rest. After the cannonball is fired, the momentum of the cannonball is m1v1 and the momentum of the cannon is m2v2, where m1 and m2 are the masses of the cannonball and the cannon respectively, and v1 and v2 are their respective velocities.
Since the initial momentum is zero, the final momentum is also zero. Therefore, m1v1 + m2v2 = 0. Plugging in the given values, we have (20 kg)(v1) + (2.40 x 10^3 kg)(-3.5 m/s) = 0. Solving for v1, we find v1 = 420 m/s. Therefore, the velocity of the cannonball is 420 m/s.
14.
A 50.0 g shell fired from a 3.00 kg rifle has a speed of 400.0 m/s. With what speed does the rifle recoil in the opposite direction?
Correct Answer
A. 6.67 m/s
Explanation
When a bullet is fired from a rifle, according to Newton's third law of motion, the bullet exerts a force on the rifle and the rifle exerts an equal and opposite force on the bullet. This means that the momentum gained by the bullet in one direction is balanced by the momentum gained by the rifle in the opposite direction.
To find the speed at which the rifle recoils, we can use the principle of conservation of momentum. The momentum of the bullet is given by the product of its mass and velocity, which is (50.0 g) * (400.0 m/s). The momentum of the rifle can be calculated by multiplying its mass (3.00 kg) with its velocity, which we need to find.
Since the total momentum before the bullet is fired is zero, the total momentum after the bullet is fired should also be zero. Therefore, we can set up the equation:
(mass of bullet * velocity of bullet) + (mass of rifle * velocity of rifle) = 0
Solving for the velocity of the rifle, we get:
(50.0 g * 400.0 m/s) + (3.00 kg * velocity of rifle) = 0
Rearranging the equation and solving for the velocity of the rifle, we find that it is approximately 6.67 m/s.