Newton’s Laws

Basics
Sir Isaac Newton (1642-1726) was a genius who figured out many principles of mathematics and science.

Purportedly inspired by an apple falling from a tree, Newton has been credited with the discovery of gravity.

Newton’s Three Laws of Motion are commonly known as Newton’s Laws.

Of the three laws, Newton’s Second Law most readily lends itself to test questions.  You might or might not be given its associated formula.

Newton’s First Law

An object at rest remains at rest (unless acted upon by an external force).
An object in motion remains in motion (unless acted upon by an external force).

Inertia = tendency of an object at rest to remain at rest or of an object in motion to remain in motion.

Newton’s Second Law

Force = Mass × Acceleration
F = ma

F = force
(often measured in Newtons [N])

m = mass
(often measured in kilograms [kg])

a = acceleration
(often measured in meters per second per second [m/s²])

Of the three laws, Newton’s Second Law most readily lends itself to test questions (involving the calculator).  You might or might not be given its associated formula.

Newton’s Third Law

For every action, there is an equal and opposite reaction.

Question
Given F = ma, what happens to F when m doubles and a remains constant (unchanged)?

F doubles.

F = 2m × a = 2ma
Because F is directly proportional to the doubling of m when a remains constant, F doubles.

Question

Given F = ma, what happens to F when m remains constant (unchanged) and a is halved?

F is cut in half.

F = m × $\bf\displaystyle\frac{a}{2}$$\bf\displaystyle\frac{ma}{2}$
Because F is directly proportional to the halving of a when m remains constant, F decreases to half of its former self.

Question

Given F = ma, what happens to F when m doubles and a is halved?

F remains the same.

F = 2m × $\bf\displaystyle\frac{a}{2}$ = $\bf\displaystyle\frac{2ma}{2}$ = ma
Because F is directly proportional to m and a, when m doubles and a is cut in half,
F remains the same.

Question

Given F = ma, what happens when F remains constant (unchanged) and m is halved?

a doubles.

F = $\bf\displaystyle\frac{m}{2}$ × 2a =  $\bf\displaystyle\frac{2ma}{2}$ = ma
Because F is directly proportional to m and a, when F remains constant and m is cut in half, a must double.

Question

Given F = ma, what happens when F remains constant (unchanged) and a triples?

m decreases to a third of its former self.

F = 3a × $\bf\displaystyle\frac{m}{3}$$\bf\displaystyle\frac{3am}{3}$ = am = ma
Because F is directly proportional to m and a, when F remains constant and a triples, m must decrease to a third of its former self.

Question

A car with a mass of 2000 kg accelerates at 3 m/s².
What force was applied to the car?

6000 N

See Plug-In.
m = 2000 kg
a = 3 m/s²
F = ma
F = 2000 × 3 = 6000

Input Display Comment
2000 × 3 2000*3 F = ma
Plug in 2000 for m.
Plug in 3 for a.
Newton’s Second Law

Practice – Questions

1.  Given F = ma, what happens to F when m triples and a remains constant?
A.  F remains the same.
B.  F doubles.
C.  F decreases to a third of its former self.
D.  F triples.

2.  Given F = ma, what happens to F when m remains constant and a is decreased to a third of its former self?
A.  F remains the same.
B.  F doubles.
C.  F decreases to a third of its former self.
D.  F triples.

3.  Given F = ma, what happens when F remains constant and m is decreased to a fourth of its former self?
A.  a remains the same.
C.  a decreases to a fourth of its former self.
D.  a doubles.

4.  Given F = ma, what happens when F remains constant and a doubles?
A.  m is cut in half.
B.  m doubles.
C.  m remains the same.
D.  m triples.

5.  A car with a mass of 4000 kg accelerates at 1.5 m/s².
What force was applied to the car?
A.  4000 N
B.  1500 N
C.  3000 N
D.  6000 N