Question

Newton’s First Law of Motion
Newton’s first law of motion states that the motion of an object does
not change as long as the net force acting on the object is zero. In
other words, an object at rest tends to remain at rest, and an object in
motion tends to remain in motion. For example, a soccer ball lying on
the ground does not move until a force, such as a kick, causes it to
move. Once in motion, it will continue to move until another force,
such as friction or a wall, causes it to slow down or stop. Newton’s
first law is also called the law of inertia. Inertia is the tendency of an
object to resist a change in its motion.
Newton’s Second Law of Motion
Objects change their motion, or accelerate, when unbalanced forces
are applied to them. For example, if a rolling soccer ball starts to roll
up a slope, it will decrease in velocity until it stops. Then, it will roll
back down the slope at an increasing velocity. Two forces—inertia and
gravity—are acting on the ball. They are acting together when the ball
is rolling down the slope and against each other when the ball is
rolling up the slope. Their combined force on the ball is the net force.
Newton’s second law of motion states that the acceleration of an
object is equal to the net force acting on it divided by the object’s
mass. Mass is a measure of the inertia of an object and depends on
the amount of matter the object contains. Newton’s second law can be
expressed by the equation:
Acceleration
, or a
An object with less mass or greater net force has greater acceleration.
Weight
Weight is the force of gravity acting on an object. The equation for
weight is:
Weight Mass
Acceleration due to gravity, or W
mg
Acceleration due to gravity (g) is 9.8 m/s2.
F
m
Net force
Mass

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Section 12.2 Newton’s First and Second Laws of Motion
Solved Examples
Example 1:
Erin threw a 3.0-kilogram ball with a net force of
210 newtons. What was the ball’s acceleration?
Given: Net force (F)
210 N
Mass (m)
3.0 kg
Unknown: Acceleration (a)
Equation: a
Solution: a
70 N/kg
The answer, 70 N/kg, can also be expressed as 70 m/s2,
because the unit N/kg equals m/s2.
Example 2:
A 1,200-kilogram car accelerates at 4.5 m/s2. What is
the net force of the car?
Given: Mass (m)
1,200 kg
Acceleration (a)
4.5 m/s2
4.5 N/kg
Unknown: Net force (F)
Equation: a
Solution: Solve the equation for F, and substitute the
given values:
F
a
m; F
4.5 N/kg
1,200 kg
5,400 N
Example 3:
Find the mass of a person whose weight is 490 N.
Given: Weight (W)
490 N
Acceleration due to gravity (g)
9.8 m/s2
9.8 N/kg
Unknown: Mass (m)
Equation: W
mg
Solution: Solve the equation for m, and substitute the
given values:
m
; m
50 kg
490 N
9.8 N>kg
W
g
F
m
210 N
3.0 kg
F
m
Physical Science Math Skills and Problem Solving Workbook
43

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44
Physical Science Math Skills and Problem Solving Workbook
Practice Exercises
Exercise 1: What is the acceleration of a 1,500-kilogram truck with
a net force of 7,500 newtons?
Exercise 2:
A runner with a mass of 60 kilograms accelerates at
2.2 m/s2. What is the runner’s net force?
Exercise 3:
Find the mass of a flying discus that has a net force of
1.05 newtons and accelerates at 3.5 m/s2.
Exercise 4:
Ian has a mass of 58.0 kilograms. What is his weight?
Exercise 5:
Find the mass of a book that has a weight of
14.7 newtons.

Answer 1

Here are the solutions.

Exercise 1
Given: F = 7,500 N, m = 1,500 kg
a = F/m = 7,500 / 1,500 = 5.0 m/s²

Exercise 2
Given: m = 60 kg, a = 2.2 m/s²
F = m a = 60 × 2.2 = 132 N

Exercise 3
Given: F = 1.05 N, a = 3.5 m/s²
m = F / a = 1.05 / 3.5 = 0.30 kg

Exercise 4
Given: m = 58.0 kg, g = 9.8 m/s²
W = m g = 58.0 × 9.8 = 568 N (568.4 N)

Exercise 5
Given: W = 14.7 N, g = 9.8 m/s²
m = W / g = 14.7 / 9.8 = 1.50 kg