(FOM) Newton's 2nd Law of Motion Lesson

Newton's 2nd Law of Motion

We are now ready to look at Newton's 2^nd Law. Let's begin by watching the following video created by the European Space Agency.

Newton's 2^nd Law of Motion mathematically states the cause-and-effect relationship between force and acceleration. It states that the acceleration of a system is directly proportional to and in the same direction as the net external force acting on the system, and inversely proportional to its mass. In other words, this equation tells us that an object subjected to an external force will accelerate and that the amount of acceleration is proportional to the size of the force. The greater the force, the greater the acceleration will be. The amount of acceleration is also inversely proportional to the mass of the object; for equal forces, a heavier object will experience less acceleration than a lighter object.

2nd Law Visual:
Given the Same Mass:
F means a
A large force means large acceleration.
F means a
A small force means small acceleration.
Given the same Force
m means a
A small mass means large acceleration.
m means a
A large mass means small acceleration.

You have seen this law in effect since you were a baby. To exemplify this law, let's think about a grocery cart. With the same amount of stuff (mass) in your cart, if you push your cart with a large force then the cart will have a large acceleration. However, if you push your cart with a small force then the cart will have a small acceleration. Continuing, if we change the mass but use the same force then we will also see an effect on the acceleration. If you have an empty cart and apply a force then it will accelerate much quicker than if you have a totally full cart applying the same force.

Newtons 2nd Law. with m, a, F indicated

Newton's 2^nd Law Equation:

F_net = m * a

You will be required to find all of the variables given in the equation. If you would like help rearranging the equation, then use the given triangle below.

Velocity Triangle: How to use: Cover the variable you are solving for with your hand. The remaining variables will either be multiplied or divided as shown by the image.
Resulting Equations:
Force = mass x acceleration
mass = force / acceleration
acceleration = force / mass

Let's look at a couple of example problems:

How much force is needed to accelerate a truck with a mass of 2,000 kilograms at a rate of 3m/sec²?

Looking For:

Force

Solution:

F_net = m * a

F_net = 2000 kg * 3 m/s²

F = 6,000 N

Given:

Mass = 2,000 kg

Acceleration = 3 m/s²

Equation:

F_net = m * a

What is the mass of an object that requires 15 N to accelerate it at a rate of 1.5 m/sec²?

Looking For:

Mass

Solution:

$LaTeX: m=\frac{F}{a}$ $m=\frac{F}{a}$

$LaTeX: m=\frac{15 N}{15mis^2}=10\:kg$ $m=\frac{15 N}{15mis^2}=10\:kg$

m = 10 kg

Given:

Force = 15 N

Acceleration = 1.5 m/s²

Equation:

Practice Problems

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