# Newton’s Law of Motion

The First Law of Motion states, “A body at rest will remain at rest, and a body in motion will remain in motion unless it is acted upon by an external force.”

This simply means that things cannot start, stop, or change direction all by themselves. It takes some force acting on them from the outside to cause such a change. This property of massive bodies to resist changes in their state of motion is sometimes called inertia.

Note: The more mass an object has, the more inertia an object has.

The Second Law of Motion describes what happens to a massive body when it is acted upon by an external force.

It states, “The force acting on an object is equal to the mass of that object times its acceleration.” This is written in mathematical form as F = ma, where F is force, m is mass, and a is acceleration.

The bold letters indicate that force and acceleration are vector quantities, which means they have both magnitude and direction. The force can be a single force, or it can be the vector sum of more than one force, which is the net force after all the forces are combined.

Note: If the object moves at a constant velocity, then there is no acceleration (a = 0), therefore, no force is acting on the object.

When a constant force acts on a massive body, it causes it to accelerate, i.e., to change its velocity, at a constant rate. In the simplest case, a force applied to an object at rest causes it to accelerate in the direction of the force.

However, if the object is already in motion, or if this situation is viewed from a moving reference frame, that body might appear to speed up, slow down, or change direction depending on the direction of the force and the directions that the object and reference frame are moving relative to each other.

The Third Law of Motion states, “For every action, there is an equal and opposite reaction.”

This law describes what happens to a body when it exerts a force on another body. Forces always occur in pairs, so when one body pushes against another, the second body pushes back just as hard.

For example, when you push a cart, the cart pushes back against you; when you pull on a rope, the rope pulls back against you; when gravity pulls you down against the ground, the ground pushes up against your feet; and when a rocket ignites its fuel behind it, the expanding exhaust gas pushes on the rocket causing it to accelerate.

## Practice Problems:

1. Determine the accelerations that result when a 12-N net force is applied to a 3-kg object.

Ans: F = ma
a = F/m = 12/3 = 4 m/s

2. A net force of 15 N is exerted on an encyclopedia to cause it to accelerate at a rate of 5 m/s. Determine the mass of the encyclopedia.

Ans: m = F/a = 15/5 = 3 kg

3. Ben pushes a suitcase with a horizontal force of 50.0 N at a constant speed of 0.5 m/s for a horizontal distance of 35.0 meters. How much force is the suitcase exerting on Ben during this entire motion?

Ans: 50.0 N on Ben in the direction opposite the movement of Ben’s push.

4. An accelerating body has a net force acting on it. True or False?

Ans: True.

5. A car going about a roundabout has a net force acting on it. True or False?

Ans: True. Changing direction is changing acceleration which only occurs if there is a net force causing the change in direction. In this scenario, there is a constant perpendicular force from the side that is causing this change of direction.