Newton's Second Law of Motion

Newton's second law of motion states that "the acceleration of an object varies directly as the force exerted to the object and inversely to the mass of the object." The second law explains how the force and the mass of an object affects its acceleration, thus, the second law is also named as the Law of Acceleration. The law can be expressed mathematically as

$$a=\frac Fm$$

where $$a$$ is the acceleration of the object, $$F$$ is the force applied to the object and $$m$$ as the mass of the object.

The unit for force is $$N=kg \cdot m/s^2$$ and the unit for mass is $$kg.$$ giving the unit for acceleration as

$$a=\frac{kg \cdot m/s^2}{kg}=m/s^2.$$

The unit for acceleration is $$m/s^2.$$

Example 1.

Jon is planning to rearrange his bedroom. He pushed his bed to the right side of the room with a force of 150 N. If his bed has a mass of 85 kg, what is the acceleration of the bed?

Given:

Force applied by Jon in pushing his bed = 150 N

Mass of the bed = 85 kg

Solution.

To solve for the acceleration of the bed, we just simply substitute the given values to the equation of the law, thus

$$a=\frac Fm=\frac{150\;N}{85\;kg}=1.76\;m/s^2$$.

Example 2.

Izrafel is riding his bicycle when suddenly a dog runs across the street. If the bicycle is accelerating at a rate of $$4.2\;m/s^2$$, how much force is needed to stop it so that it will not hit the dog? Assuming that his mass and the bike's has a sum of 56 kg.

Given: $$a=4.2\;m/s^2\\ m=56\;kg$$

Solution:

$$F=ma=(56\;kg)(4.2\;m/s^2)=235.2\;N$$

Izrafel needed a force of 235.2 N to immediately stop the bike and avoid hitting the dog.

Example 3.

A frisbee player applied 350 N of force to the disc causing it to accelerate at $$2.0 \times 10^3\;m/s^2.$$ What is the disc's mass?

Given: $$F=350\;N\\ a=2.0 \times 10^3$$

Solution:

The mass can be calculated using the formula

$$m=\frac Fa=\frac{350\;N}{2.0 \times 10^3\;m/s^2}=0.175\;kg$$

thus, the disc's mass is 0.175 kg