Newton's Second Law

Newton's Second Law is one of the most famous of all things in the realm of physics. It is fundamental to so many aspects of physics, architecture, and engineering that it is hard to find anything that equally ranks in prominence.

Stated with words, Newton's Second Law says that if an object accelerates (if it changes magnitude or direction of its velocity), the force required is equal to the mass of the object times the rate of acceleration. 

So, to state that in less fancy terms… Say something is being pushed. If you push something, it's going to change velocity. (That could mean starting or stopping.) So, if you recall that changing velocity is the same as accelerating, then when you push something it accelerates. The harder you push, the faster it accelerates. The heavier it is, the slower it accelerates. 

Yet again, logic and common since prove true! If you just stop and think about it, you already understand this.

Just for fun, let's reprise…

If something has a lot of mass, it will change velocity less under a given force than if the same force is applied to something with less mass. The stronger the force, the faster an object will accelerate.

Naturally, since this is physics, there is a formula that models the relationship between mass, force, and acceleration. Where F is force, a is acceleration, and m is mass, then:

F = ma

This leads to a couple of derived formulas, just in case finding m or a is desired.

To find F:

F = ma

To find m:

m = F/a

To find a:

a = F/m

EXAMPLE 1:

Find the force needed to to cause a 5 kg object to accelerate at a rate of 20 (m/s)/s to the left.

F = find it

m = 5 kg

a = 20 (m/s)/s Left

F = ma

F = 5•20

F = 100 N Left

EXAMPLE 2:

If a 20 N force to the Right is applied to an object and causes it to accelerate at a rate of 4 (m/s)/s, what is the mass of the object?

F = 20 N Right

m = find it

a = 4 (m/s)/s

F = ma

20 = 4•m

20/4 = m

5 kg = m

OR

m = F/a

m = 20/4

m = 5 kg

EXAMPLE 3:

If a 15 N force to the Right is applied to a 3 kg object, what will the rate of acceleration be?

F = 15 N Right

m = 3 kg

a = find it

F = ma

15 = 3•a

15/3 = a

5 (m/s)/s = a

OR

a = F/m

a = 15/3

a = 5 (m/s)/s 

Summary

Using Newton's Second Law effectively allows demonstrating the relationship between mass, acceleration, and force. It follows logic and common sense completely, and the math requires only picking out the numbers, plugging them into the equation and using multiplication and division to solve for the missing variables.