3B5 Linear Momentum and Impulse

Question 1

Define:

Linear momentum

Answer 1

It is the quantity of motion of an object, defined as the product of its mass and velocity. It has both magnitude and direction.

Represented as p=mv, where p is momentum, m is mass, and v is velocity.

Question 2

Fill in the blank:

Momentum is a _____ quantity.

Answer 2

Vector

Momentum’s direction aligns with the velocity of the object.

Question 3

Fill in the blank:

Momentum depends on both _____ and _____.

Answer 3

mass; velocity

Since momentum is calculated as 𝑝=𝑚𝑣, increasing either mass or velocity results in greater momentum. This explains why heavier or faster-moving objects are harder to stop.

Question 4

A cue ball with a mass of 0.50 kg is moving at 0.10 m/s. Calculate its linear momentum.

Answer 4

0.05kg m/s

The equation looks like p=0.50kg×0.10m/s. Linear momentum is the product of an object’s mass and velocity. It is a vector quantity.

Question 5

True or False:

Momentum is always conserved, even when external forces act on a system.

Answer 5

False

Momentum is only conserved in isolated systems where no external forces act.

Question 6

How are momentum (p) and kinetic energy (KE) mathematically related?

Answer 6

Momentum (p) and kinetic energy (KE) are related through the equation: KE= p²/2m

Momentum (𝑝=𝑚𝑣) depends linearly on velocity, meaning it increases proportionally with speed. In contrast, kinetic energy (𝐾𝐸 = ½𝑚𝑣²) depends on the square of velocity, meaning a small increase in speed results in a much larger increase in energy.

Question 7

What does Newton’s second law state about momentum?

Answer 7

The net force on an object is the time rate of change of the momentum: F = Δp / Δt.

This can also be expressed as F = mΔv / Δt.

Question 8

What is the SI unit of momentum?

Answer 8

kg m/s

This unit comes from p=mv, combining mass (kg) and velocity (m/s).

Question 9

State the law of conservation of momentum.

Answer 9

The total momentum of an isolated system remains constant.

This applies when no external forces are acting on the system.

Question 10

Fill in the blank:

Momentum conservation is valid only in the absence of ______ forces.

Answer 10

external

External forces disrupt the balance, changing the system’s total momentum.

Question 11

How does a game of billiards represent the concept of momentum conservation in real life?

Answer 11

The momentum of the cue ball is transferred to other balls upon impact.

Friction and spin may slightly alter the outcome.

Question 12

How does the law of conservation of momentum explain rocket propulsion?

Answer 12

Rockets eject mass backward to create forward momentum, conserving the system’s total momentum.

This principle underlies Newton’s third law.

Question 13

How do internal forces influence the conservation of momentum?

Answer 13

Internal forces within a system cancel out in action-reaction pairs, meaning they do not change the system’s total momentum.

Only external forces can change the total momentum.

Question 14

Under what conditions is momentum not conserved?

Answer 14

When external forces (e.g., friction, air resistance, or applied forces) act on a system, causing a net force that changes the total momentum.

Non-isolated systems do not preserve total momentum.

Question 15

List the conditions that must be satisfied for momentum conservation.

Answer 15

• The system must be isolated (no external forces).
• The total momentum before the interaction must equal the total momentum after the interaction.

Momentum conservation is a fundamental principle of physics, particularly in collisions and explosions.

Question 16

What does the equation m₁v₁=m₂v₂ represent?

Answer 16

The conservation of momentum in an isolated system involving two objects.

Specifically when an object at rest moves after an interaction (such as recoil) or when one object transfers all of its momentum to another in a special case of elastic collisions. It is commonly used in elastic collisions where no energy is lost.

Question 17

Define:

Impulse

Answer 17

Change in momentum caused by a force acting over time.

J=Δp, where J is impulse and Δp is the change in momentum.

Question 18

Explain why impulse is greater for objects with higher momentum.

Answer 18

Greater momentum requires a larger impulse for the same rate of deceleration.

This is evident in high-speed collisions.

Question 19

What role does time play in impulse?

Answer 19

Longer time duration for a force decreases the force needed for the same change in momentum.

This principle is applied in airbags and cushioned surfaces for safety.

Question 20

What is the SI unit for impulse?

Answer 20

newton-second (N⋅s)

It shares the same units as momentum (kg⋅m/s)

Question 21

What is the Impulse Momentum Theorem?

Answer 21

A force applied to an object for some amount of time causes that object’s velocity to change, or an impulse causes a change in momentum.

This is represented mathematically as J = Δp.

Question 22

How are force and impulse related?

Answer 22

Impulse (J) is the product of force (F) and the time interval (Δt) over which it acts: J=FΔt.

Impulse also equals the change in momentum of the object.

Question 23

Why is increasing collision time beneficial in safety devices?

Answer 23

Increasing time reduces the force needed to achieve the same momentum change.

This principle is applied in airbags and helmets.

Question 24

Fill in the blank:

In a collision, impulse is the area under the ______ vs. time graph.

Answer 24

Force

The graph provides a visual representation of impulse.

Question 25

# True or False: A large **impulse** always means a large **force**.

Answer 25

False ## Footnote Impulse can also result from a small force acting over a long time.

Question 26

How does impulse apply in **baseball**?

Answer 26

A longer contact time between a bat and ball **increases the ball's final velocity**. ## Footnote The impulse-momentum relationship is critical in sports dynamics.

Question 27

# Fill in the blank: For a uniform object, the **center of mass** is located at its \_\_\_\_\_\_\_ \_\_\_\_\_.

Answer 27

Geometric center ## Footnote Irregular objects require integration or weighted averages to find the center of mass.

Question 28

How can the **center of mass** be determined for a system of **two particles**?

Answer 28

r =(m1r1+m2r2)/(m1+m2) ## Footnote In this equation, m1 and m2 are the masses, and r1 and r2 are their positions. The center of mass lies closer to the particle with greater mass.

Question 29

# Define: Rigid body

Answer 29

Object that **does not deform or change shape** when forces are applied to it. ## Footnote The distances between points within the object remain constant. Rigid bodies are idealized objects in physics used to simplify the analysis of motion.

Question 30

What is the correct approach to find the center of mass for a **rigid body**?

Answer 30

Use an integral to account for continuous mass distribution. ## Footnote For example, this applies to calculating the center of mass for a graduated cylinder filled with water.

Question 31

# True or False: The **center of mass** always lies within the object.

Answer 31

False ## Footnote For hollow or irregularly shaped objects, the center of mass can lie outside the object.

Question 32

Where is the center of mass located in a **donut**?

Answer 32

Within the **empty space** in its donut hole. ## Footnote This contrasts with a human's center of mass, which lies within the body.

Question 33

What happens to the **center of mass** when a system moves?

Answer 33

The center of mass **follows the same trajectory** as if the total external forces acted on it alone. ## Footnote This simplifies motion analysis in systems like rockets.

Question 34

What is the relation between the **center of mass** and **linear momentum**?

Answer 34

The total linear momentum of a system is the product of the system's total mass and the velocity of its center of mass: **p**=M**v**. ## Footnote M is the total mass, and **v** is the velocity of the center of mass.

Question 35

How is the **center of mass** related to **impulse**?

Answer 35

The impulse applied to a system equals the change in momentum of the center of mass:**J**=MΔ**v**. ## Footnote External forces change the motion of the center of mass via impulse.