Question 1

Conservation of momentum: A baseball is thrown vertically upward and feels no air resistance. As it is rising

Accepted Answer

Momentum is not conserved for the baseball because the force of gravity acts on it, changing its velocity as it rises. However, mechanical energy (the sum of kinetic and potential energy) is conserved because there is no air resistance to dissipate the energy.

Question 2

Impulse-momentum: A stationary 1.67-kg object is struck by a stick. The object experiences a horizontal force given by F = at - bt², where t is the time in milliseconds from the instant the stick first contacts the object. If a = 1500 N/(ms) and b = 20 N/(ms)², what is the speed of the object just after it comes away from the stick at t = 2.74 ms?

Accepted Answer

Impulse = change in momentum$$Ft = mv_f - mv_i$$$$(1500t - 20t^2)ms = (1.67kg)v_f - 0$$$$v_f = 900t - 12t^2$$$$v_f = 900(2.74) - 12(2.74)^2 = 3.3m/s$$

Question 3

Center of mass: There must be equal amounts of mass on both side of the center of mass of an object.

Accepted Answer

The statement is incorrect. The center of mass of an object is the point where the entire mass of the object can be assumed to be concentrated. There may not be equal amounts of mass on both sides of the center of mass, depending on the distribution of mass within the object.

Question 4

Impulse: A time-varying horizontal force F(t) = At⁴ + Bt² acts for 0.500 s on a 12.25-kg object, starting at time t = 1.00 s. In the SI system, A has the numerical value 4.50 and B has the numerical value 8.75. (a) What are the SI units of A and B? (b) What impulse does this force impart to the object?

Accepted Answer

The answer of Impulse: A time-varying horizontal force F(t) =...

Question 5

Conservation of momentum: 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?

Accepted Answer

Catching the ball will minimize your speed because the momentum is shared between you and the ball, whereas deflecting it back transfers more momentum to you, increasing your speed.

Question 6

Explosions in one dimension: 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

Accepted Answer

The lighter block will have more kinetic energy because kinetic energy is inversely proportional to mass when momentum is conserved. Since both blocks have equal and opposite momentum, the lighter block will have more kinetic energy.

Question 7

Impulse-momentum: 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?

Accepted Answer

Explanation:The change in momentum of the ball is:$$p_f-p_i=mv_f-mv_i$$$$=(0.500	ext{ kg})(20.0	ext{ m/s})-(0.500	ext{ kg})(-14.0	ext{ m/s})$$$$=18.4	ext{ kg}\cdot	ext{m/s}$$The change in momentum of the stone is equal in magnitude but opposite in direction to the change in momentum of the ball, so the magnitude of the change in momentum of the stone is also 18.4 kg∙m/s.

Question 8

Collisions: In an INELASTIC collision between two objects

Accepted Answer

In an inelastic collision, kinetic energy is not conserved because some of it is transformed into other forms of energy such as heat or sound. Although kinetic energy is not conserved, momentum is always conserved in any type of collision. Therefore, the momentum of the system is conserved, but the kinetic energy of the system is not conserved in an inelastic collision.

Question 9

Collisions: In a perfectly ELASTIC collision between two perfectly rigid objects

Accepted Answer

In a perfectly elastic collision, both momentum and kinetic energy are conserved. Momentum is conserved because the total momentum of the system before the collision equals the total momentum of the system after the collision. Kinetic energy is conserved because in an elastic collision, no energy is lost due to heat or deformation of the objects.

Question 10

Impulse-momentum: 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?

Accepted Answer

Using the impulse-momentum theorem, we have:

$$	ext{Impulse} = 	ext{Change in momentum}$$

$$	ext{Force} 	imes 	ext{Time} = \Delta 	ext{p} = 	ext{p}_{	ext{f}} - 	ext{p}_{	ext{i}}$$

$$	ext{Force} = \frac{\Delta 	ext{p}}{	ext{Time}} = \frac{	ext{p}_{	ext{f}} - 	ext{p}_{	ext{i}}}{	ext{Time}}$$

where $\Delta 	ext{p}$ is the change in momentum and $	ext{Time}$ is the time the ball was in contact with the wall.

We can calculate the change in momentum as:

$$\Delta 	ext{p} = 	ext{p}_{	ext{f}} - 	ext{p}_{	ext{i}} = 	ext{m}(	ext{v}_{	ext{f}} - 	ext{v}_{	ext{i}})$$

Plugging in the given values:

$$\Delta 	ext{p} = 0.200 	ext{ kg} 	imes (12.0 	ext{ m/s} - (-20.0 	ext{ m/s})) = 6.40 	ext{ kg m/s}$$

And the time given is $	ext{Time} = 60.0 	ext{ ms} = 0.060 	ext{ s}$.

Substituting these into the equation for force:

$$	ext{Force} = \frac{\Delta 	ext{p}}{	ext{Time}} = \frac{6.40 	ext{ kg m/s}}{0.060 	ext{ s}} = 107 	ext{ N}$$

Therefore, the magnitude of the average force applied to the ball is 107 N. The answer is (B).

Question 11

Explosions in one dimension: A shell explodes into two fragments, one fragment 25 times heavier than the other. If any gas from the explosion has negligible mass, then

Accepted Answer

EC) In an explosion, the total momentum of the system (shell) must be conserved. Before the explosion, the shell's momentum is zero (assuming it's at rest), so the total momentum after the explosion must also be zero. This means the momentum gained by the lighter fragment must be equal in magnitude and opposite in direction to the momentum gained by the heavier fragment, making their momentum changes exactly the same.E) The kinetic energy change of the lighter fragment is greater than that of the heavier fragment because, for a given momentum change, lighter objects acquire a higher velocity than heavier objects. Since kinetic energy depends on the square of the velocity ($KE = \frac{1}{2}mv^2$), the lighter fragment, having a higher velocity for the same momentum change, will have a disproportionately larger increase in kinetic energy. However, the exact ratio of their kinetic energy changes depends on their velocities and cannot be determined to be exactly 25 times greater without additional information. This choice is included based on the options provided, but it's important to note the explanation for why the kinetic energy change of the lighter fragment is greater, not necessarily exactly 25 times as great.

Question 12

Collisions: A small car has a head-on collision with a large truck. Which of the following statements concerning the magnitude of the average force due to the collision is correct?

Accepted Answer

According to Newton's third law of motion, for every action, there is an equal and opposite reaction. This means that the magnitude of the force on the truck is equal to the magnitude of the force on the car during the collision.

Question 13

Explosions in one dimension: 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  to separate the two canoes. If we can neglect any resistance due to the water, what is correct to say about the final momentum and kinetic energy of the system consisting of the two canoes and the two men inside?

Accepted Answer

The answer of Explosions in one dimension: Jacques and George...

Question 14

Collisions: In a collision between two objects having unequal masses, how does magnitude of the impulse imparted to the lighter object by the heavier one compare with the magnitude of the impulse imparted to the heavier object by the lighter one?

Accepted Answer

According to the Law of Conservation of Momentum, the total momentum of the system before and after the collision remains constant. Therefore, the impulse imparted to one object is equal and opposite to the impulse imparted to the other object. In a collision between two objects having unequal masses, the magnitude of the impulse imparted to the lighter object by the heavier one is the same as the magnitude of the impulse imparted to the heavier object by the lighter one. Therefore, both objects receive the same impulse.

Question 15

Conservation of momentum: 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?

Accepted Answer

The answer of Conservation of momentum: On a smooth horizontal...

Question 16

Momentum: 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?

Accepted Answer

The answer of Momentum: A firecracker breaks up into several...

Question 17

Impulse-momentum: Consider two less-than-desirable options. In the first you are driving 50 km/h and crash head-on into an identical car also going 50km/h. In the second option you are driving 50 km/h 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?

Accepted Answer

The impact force experienced in both scenarios would be the same if the collision time is the same. This is because the change in momentum (impulse) would be identical in both cases, assuming the car stops in both scenarios, leading to the same force experienced due to the impulse-momentum theorem.

Question 18

Conservation of momentum: A small glider is coasting horizontally when suddenly a very heavy piece of cargo falls out of the bottom of the plane. You can neglect air resistance. Just after the cargo has fallen out

Accepted Answer

The conservation of momentum states that the total momentum of a system before an event is equal to the total momentum after the event, as long as there are no external forces acting on the system. In this case, the system consists of the small glider and the heavy cargo before and after the cargo falls out. Since there are no external forces acting on the system, the total momentum of the system must remain constant. Therefore, the small glider will not speed up or slow down, and the cargo will not speed up or slow down. Thus, the answer is C.

Question 19

Conservation of momentum: As a tile falls from the roof of a building to the ground its momentum is conserved.

Accepted Answer

Conservation of momentum only applies in a closed system where there are no external forces acting on the system. In the case of the falling tile, the external force of gravity is acting on it, so its momentum is not conserved.

Question 20

Impulse: A 2.50-kg stone is dropped from rest at a height of 3.75 m. What impulse does gravity impart to this stone from the instant it is dropped until it hits the ground, assuming negligible air resistance?

Accepted Answer

The answer of Impulse: A 2.50-kg stone is dropped from...

Quiz 7: Potential Energy and Energy Conservation