Question

Momentum is the product of an object’s mass and velocity. The larger
the mass of an object or the faster it is moving, the larger its
momentum. If an object has large momentum, it is hard to stop.
Imagine trying to stop a car rolling very slowly down a slope. It
would be hard to do because of the large mass of the car, not because
of the car’s velocity. It would also be hard to stop an object with a
small mass but great velocity, such as a baseball traveling more than
100 kilometers per hour. The baseball’s speed would give it large
momentum.
Momentum Formula
The formula for calculating the momentum of an object is:
Momentum Mass
Velocity
Momentum is measured in units of kilogram-meters per second,
written kg·m/s. For example, the momentum of a golf ball with a
mass of 0.05 kilograms and a speed of 58 meters per second is:
Momentum
0.05 kg
58 m/s
2.9 kg·m/s
The equation for momentum can be rewritten to find mass or
velocity if momentum is known:
Mass
Velocity
Law of Conservation of Momentum
According to the law of conservation of momentum, within a system
total momentum does not change. If one object loses momentum,
another object gains momentum. Thus, momentum is conserved. For
example, a baseball bat loses velocity and momentum when it hits a
ball. However, the ball gains velocity and momentum when the bat
strikes it.
Momentum
Mass
Momentum
Velocity

Name
Class
Date
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ved.
Section 12.3 Newton’s Third Law of Motion and Momentum
Data
A teacher is demonstrating the relationship between velocity and
momentum. She drops a 0.03-kilogram object from the school roof to
the lawn below. The graph shows the momentum of the object from
the time it leaves the roof until it lands on the lawn.
Momentum of 0.03-kg Object in Free Fall
The table shows the momentum of several cars. Each has a different
mass, but all are traveling at the same constant velocity.
Momentum of Cars with a Velocity of 20 m/s
Car
Mass (kg)
Momentum (kg·m/s)
Car A
1,400
28,000
Car B
?
27,200
Car C
1,280
25,600
Car D
1,140
?
Car E
1,050
21,000
46
Physical Science Math Skills and Problem Solving Workbook
Name
Class
Date
Momentum (milliLiters)
1.00
0.90
0.80
0.70
0.60
0.50
0.40
0.30
0.20
0.10
0
Time (s)
0.5
1.0
1.5
2.0
2.5
3.0

Name
Class
Date
© by Savvas Learning Company LLC., publishing as Pearson Prentice Hall. All rights reser
ved.
Questions
1. a. Describing Based on the graph, describe how momentum
changes with time for an object in free fall.
b. Calculating Use the object’s momentum and mass to calculate
its velocity at 1.0 second and 3.0 seconds.
c. Relating Cause and Effect What causes the momentum of the
object to change as it falls?
2. a.
Identifying Identify the car with the smallest momentum and
the car with the largest momentum. What is the mass of each of
these cars?
b. Calculating Based on its momentum and velocity, calculate the
mass of car B. Based on its mass and velocity, calculate the
momentum of car D.
c. Controlling Variables How could you increase the momentum
of car E to equal the momentum of car A?

Answer 1

1.
a. Describing — The object’s momentum increases steadily (approximately linearly) with time while it is in free fall. The points on the graph rise at a constant rate.

b. Calculating — Use p = m v and for free fall v = g t (g = 9.8 m/s^2).
- At t = 1.0 s: p = m v = 0.03 kg × (9.8 m/s) = 0.294 kg·m/s. v = p/m = 0.294/0.03 = 9.8 m/s.
- At t = 3.0 s: p = 0.03 × (9.8×3) = 0.03 × 29.4 = 0.882 kg·m/s. v = 0.882/0.03 = 29.4 m/s.

c. Relating cause and effect — The momentum changes because gravity produces a constant downward acceleration (an unbalanced external force), which increases the object’s velocity and therefore its momentum.

2.
a. Identifying — Largest momentum: Car A = 28,000 kg·m/s (mass 1,400 kg). Smallest momentum: Car E = 21,000 kg·m/s (mass 1,050 kg).

b. Calculating —
- Mass of Car B = p/v = 27,200 / 20 = 1,360 kg.
- Momentum of Car D = m v = 1,140 × 20 = 22,800 kg·m/s.

c. Controlling variables — To make Car E’s momentum equal Car A’s (28,000 kg·m/s):
- Increase Car E’s velocity to p/m = 28,000 / 1,050 ≈ 26.67 m/s (so raise speed from 20 to ≈26.7 m/s), or
- Increase Car E’s mass to p/v = 28,000 / 20 = 1,400 kg (add 350 kg to its mass).