Momentum and Collisions: Master the Fundamentals of Classical Mechanics

Question 1

In an elastic head-on collision, a 2 kg object traveling at 3 m/s collides with a 4 kg object initially at rest. Determine the velocity of the 4 kg object after the collision.

Accepted Answer

1.5 m/s

Answer

3 m/s

Answer

6 m/s

Answer

0 m/s

Question 2

Which type of collision results in the conservation of both momentum and kinetic energy?

Accepted Answer

Perfectly elastic collision

Answer

Completely inelastic collision

Answer

Inelastic collision

Answer

Perfectly inelastic collision

Question 3

A vertically launched ball reaches its maximum height. At this point, its momentum is:

Accepted Answer

Zero

Answer

Equal to its momentum at the launch point

Answer

Equal to its maximum kinetic energy

Answer

Equal to its maximum potential energy

Question 4

Which statement accurately describes the conservation of momentum and kinetic energy in different types of collisions?

Accepted Answer

Both momentum and kinetic energy are conserved in elastic collisions.

Answer

Momentum is conserved in all collisions, but kinetic energy may not be conserved.

Answer

Kinetic energy is conserved in elastic collisions, but momentum may not be conserved.

Answer

Neither momentum nor kinetic energy is conserved in any type of collision

Question 5

The principle of conservation of momentum states that:

Accepted Answer

The total linear momentum of an isolated system remains constant.

Answer

The total linear momentum of a system can change if an external force is applied.

Answer

The momentum of individual particles within a system can be negative.

Answer

Momentum is conserved only when objects are moving at constant velocities.

Question 6

In an elastic collision, both:

Accepted Answer

Kinetic energy and linear momentum are conserved.

Answer

Only momentum is conserved.

Answer

Only kinetic energy is conserved.

Answer

Neither kinetic energy nor momentum is conserved.

Question 7

Impulse is defined as:

Accepted Answer

The change in momentum of an object over a time interval.

Answer

The force acting on an object over a time interval.

Answer

The average velocity of an object over a time interval.

Answer

The mass of an object multiplied by its acceleration.

Question 8

Which type of collision involves the conversion of kinetic energy into other forms of energy, such as heat or sound?

Accepted Answer

Inelastic

Answer

Elastic

Answer

Perfectly inelastic

Answer

Completely elastic

Question 9

In a perfectly inelastic collision, the colliding objects:

Accepted Answer

Stick together and move with a common velocity.

Answer

Rebound with the same speed.

Answer

Transfer some kinetic energy to heat or other forms.

Answer

Separate without any momentum loss.

Question 10

In a head-on collision between two objects of equal mass, which statement is true?

Accepted Answer

The objects exchange equal amounts of momentum.

Answer

The objects exchange unequal amounts of momentum.

Answer

The heavier object always gains more momentum.

Answer

The lighter object always loses more momentum.

Question 11

The term 'recoil' in the context of collisions refers to:

Accepted Answer

The backward motion of an object after a collision

Answer

The forward motion of an object after a collision

Answer

The change in momentum of an object after a collision

Answer

The energy lost during a collision

Question 12

In a perfectly elastic head-on collision between a 2 kg ball moving at 5 m/s and a stationary 1 kg ball, what is the post-collision velocity of the 2 kg ball?

Accepted Answer

3.33 m/s

Answer

2.5 m/s

Answer

4 m/s

Answer

5 m/s

Question 13

In an inelastic collision, what happens to the total kinetic energy of the system?

Accepted Answer

Decreases

Answer

Increases

Answer

Remains constant

Answer

Can increase or decrease depending on the specific collision

Question 14

What is the relationship between impulse applied to an object and the change in its momentum?

Accepted Answer

Impulse is equal to the change in momentum

Answer

Impulse is twice the change in momentum

Answer

Impulse is half the change in momentum

Answer

There is no relationship between impulse and change in momentum

Question 15

Which of the following is a vector quantity?

Accepted Answer

Velocity

Answer

Mass

Answer

Temperature

Answer

Volume

Question 16

In an elastic collision, which physical quantity remains constant?

Accepted Answer

Total momentum

Answer

Kinetic energy

Answer

Total mechanical energy

Answer

Impulse

Question 17

Which of the following is not recognized as a type of collision?

Accepted Answer

Superelastic

Answer

Elastic

Answer

Inelastic

Answer

Plastic

Question 18

Impulse acting on an object is defined as:

Accepted Answer

Force multiplied by time

Answer

Change in momentum

Answer

Mass multiplied by acceleration

Answer

Kinetic energy

Question 19

A 1000 kg rocket travels at 100 m/s. How much impulse is needed to change its velocity to 200 m/s in the opposite direction?

Accepted Answer

40,000 Ns

Answer

20,000 Ns

Answer

60,000 Ns

Answer

80,000 Ns

Question 20

What is the physical definition of momentum?

Accepted Answer

Mass multiplied by velocity

Answer

Rate of change of velocity

Answer

Force acting on an object

Answer

Energy stored in an object

Question 21

Define the center of mass of a system of particles and explain its significance in understanding collision dynamics.

Accepted Answer

The center of mass of a system of particles is the point that moves with constant velocity in the absence of external forces.

Answer

The center of mass is the point where all the particles in the system are physically located.

Answer

The center of mass is the point where the net force acting on the system is zero.

Answer

The center of mass of a system of particles is always situated at the geometric center of the system.

Question 22

In an elastic collision, the total kinetic energy of the system:

Accepted Answer

Remains constant

Answer

Increases

Answer

Decreases

Answer

Varies depending on the masses of the objects

Question 23

The SI unit of impulse is:

Accepted Answer

Kilogram-meter per second (kg⋅m/s)

Answer

Newton-meter (N⋅m)

Answer

Joule (J)

Answer

Watt (W)

Question 24

Which of the following factors does NOT affect the outcome of a collision?

Accepted Answer

Temperature of the surroundings

Answer

Masses of the objects involved

Answer

Velocities of the objects involved

Answer

Coefficient of restitution

Question 25

In a perfectly inelastic collision, the objects:

Accepted Answer

Stick together and move with a common velocity

Answer

Rebound with the same speed as before the collision

Answer

Rebound with different speeds than before the collision

Answer

May not rebound at all

Question 26

A ball of mass 1 kg moving with a velocity of 10 m/s eastward collides head-on with a stationary ball of mass 2 kg. What is the velocity of the combined system after the collision?

Accepted Answer

5 m/s eastward

Answer

2.5 m/s westward

Answer

10 m/s eastward

Answer

0 m/s

Question 27

A car of mass 1000 kg traveling north at 20 m/s collides with a stationary car of mass 500 kg. The two cars stick together after the collision. What is the velocity of the combined system?

Accepted Answer

13.33 m/s north

Answer

10 m/s north

Answer

20 m/s north

Answer

5 m/s north

Question 28

Which of the following is NOT a characteristic of an elastic collision?

Accepted Answer

Kinetic energy is not conserved

Answer

Momentum is conserved

Answer

Objects rebound with the same relative speed

Answer

Objects deform minimally

Question 29

A perfectly elastic collision between two objects occurs. Which of the following statements about the kinetic energy of the system is TRUE?

Accepted Answer

The total kinetic energy of the system remains constant

Answer

The total kinetic energy of the system decreases

Answer

The total kinetic energy of the system increases

Question 30

A 2 kg object moving at 5 m/s collides head-on with a stationary 1 kg object. If the collision is perfectly elastic, what is the velocity of the 1 kg object after the collision?

Accepted Answer

10 m/s

Answer

0 m/s

Answer

5 m/s

Answer

2.5 m/s

Question 31

A 10 kg object is moving at 3 m/s. What is the momentum of the object?

Accepted Answer

30 kg m/s

Answer

30 m/s

Answer

13 kg m/s

Answer

3 kg

Question 32

In a perfectly inelastic collision between a 2 kg object moving at 4 m/s and a 3 kg object moving at -2 m/s, what is the velocity of the combined mass immediately after the collision?

Accepted Answer

1 m/s

Answer

3 m/s

Answer

-1 m/s

Answer

2 m/s

Question 33

Two objects of equal mass collide head-on and stick together. If the initial velocities of the objects are +6 m/s and -6 m/s, respectively, what is the velocity of the combined mass after the collision?

Accepted Answer

0 m/s

Answer

3 m/s

Answer

-3 m/s

Answer

6 m/s

Question 34

Two objects of equal mass collide head-on with equal and opposite velocities. If the collision is perfectly elastic, what is the total momentum of the system after the collision?

Accepted Answer

0 kg m/s

Answer

Double the initial momentum

Answer

Half of the initial momentum

Answer

The same as before the collision

Question 35

A 5 kg object is moving at 10 m/s. A constant force of 20 N is applied to the object in the direction of its motion for 2 seconds. What is the final velocity of the object?

Accepted Answer

18 m/s

Answer

28 m/s

Answer

20 m/s

Answer

12 m/s

Question 36

A system consists of two particles with masses of 2 kg and 3 kg. The 2 kg particle has a velocity of 4 m/s, and the 3 kg particle has a velocity of -2 m/s. What is the velocity of the center of mass of the system?

Accepted Answer

0.8 m/s

Answer

4 m/s

Answer

2 m/s

Answer

1 m/s

Question 37

Which of the following is the definition of linear momentum?

Accepted Answer

Mass of an object multiplied by its velocity

Answer

Energy of an object in motion

Answer

Change in velocity of an object per unit time

Answer

Force acting on an object per unit time

Question 38

A car of mass 1000 kg is traveling at 20 m/s. What is the car's momentum?

Accepted Answer

20,000 kg m/s

Answer

100,000 kg m/s

Answer

2,000 kg m/s

Answer

500 kg m/s

Question 39

Which type of collision conserves both momentum and kinetic energy?

Accepted Answer

Elastic collision

Answer

Inelastic collision

Answer

Non-collision

Answer

Perfectly inelastic collision

Question 40

In a perfectly inelastic collision, what happens to the kinetic energy of the colliding objects?

Accepted Answer

Converted to other forms of energy (e.g., heat, sound)

Answer

Fully conserved

Answer

Partially conserved

Question 41

A ball of mass 0.5 kg is thrown with a velocity of 10 m/s. It collides with a wall and bounces back with the same speed. What is the impulse experienced by the ball?

Accepted Answer

10 kg m/s

Answer

20 kg m/s

Answer

5 kg m/s

Answer

0 kg m/s

Question 42

A system consists of two particles of masses m1 = 2 kg and m2 = 3 kg. The coordinates of their positions are (1, 2) and (3, 4), respectively. What are the coordinates of the center of mass of the system?

Accepted Answer

(2, 3)

Answer

(1, 2)

Answer

(5, 6)

Answer

(3, 4)

Question 43

Which of the following is a conserved quantity in all types of collisions?

Accepted Answer

Total linear momentum

Answer

Total mechanical energy

Answer

Total kinetic energy

Answer

Total potential energy

Question 44

In an explosion, a large object breaks into two smaller objects. Which of the following statements is true about the explosion?

Accepted Answer

The total momentum of the objects before and after the explosion is the same

Answer

The total kinetic energy of the objects before and after the explosion is the same

Answer

The total potential energy of the objects before and after the explosion is the same