# Forces and Newton's Laws of Motion

## Newton’s Laws of Motion

The best pool players can predict how all the balls on the table will move once the cue ball is set into motion. They carefully control where and how hard they hit the cue ball so it moves where they want it to go. Pool balls move in predictable ways because, like all objects, they respond to forces in a certain ways.

### Forces

A force is defined as a push or pull exerted between two objects that are interacting in some way. A pool player interacts with the pool stick when he or she pushes it forward. The pool stick interacts with the cue ball when it strikes the cue ball. The cue ball may interact with other balls when it hits them. It also interacts with the table as it rolls and even when it sits motionless.

Not all forces are the same. Forces in which the two interacting objects are physically touching each other are called contact forces. The force between the pool stick and the cue ball is a contact force because the cue ball must touch the ball to push it forward. Friction is also a contact force that resists the motion of an object. Friction is a result of the fact that surfaces are not perfectly smooth, even if it appears that they are. Friction between the rolling pool ball and the table causes the ball to slow down as it rolls. Friction occurs between any objects that are touching, whether the objects are stationary, sliding, or rolling.

Forces in which the two interacting objects are not physically touching each other are known as action-at-a-distance forces. When a magnet is brought near a paper clip, the magnet exerts a force on the paper clip without having to touch it. The Moon exerts a pull on Earth’s oceans, even though the Moon is hundreds of thousands of kilometers away from Earth.

#### Newton’s First Law

In the seventeenth century, Sir Isaac Newton published three laws that explain the motion of objects. A law is a statement that describes a relationship in nature that has been observed to always occur under certain conditions. The motions of pool balls, a paper clip, the Moon, and Earth are all described by Newton’s laws of motion.

Newton’s first law of motion states that an object at rest tends to stay at rest, and an object in motion tends to stay in motion with the same velocity, unless an unbalanced force acts on it. To state means “to declare,” or “to express in words.” The combination of all the forces acting on an object is the net force. Balanced forces cancel each other to produce a zero net force. Unbalanced forces do not cancel out. When a car is parked, the forces acting on it are balanced, and it does not move. It will stay at rest until an unbalanced force is exerted on it. The forces on the car are also balanced when it is in motion with a constant velocity. It will continue moving at this velocity until an unbalanced force acts on it.

The forces on a parked car are balanced until an unbalanced force is exerted on it.

Another way of thinking of the first law of motion is that an object tends to resist any change in its motion. Inertia is the tendency of an object to resist any change in its motion. The more mass an object has, the greater its inertia.

#### Newton’s Second Law

According to Newton’s second law of motion, an object acted upon by a net force will accelerate in the direction of the force. Acceleration can be determined by the following equation:

Acceleration is measured in m/s2, net force is measured in N, and mass is measured in kg. According to the equation, the acceleration of an object produced by a net force is directly proportional to the magnitude of the net force, in the same direction as the net force, and inversely proportional to the mass of the object. This means that if two cars are acted on with the same force, the car with less mass car will have a larger acceleration. Similarly if the two cars with the same mass are acted on by two different forces, the car acted on by the larger force will have a greater acceleration.

#### Newton’s Third Law

According to Newton’s third law of motion, when one object exerts a force on a second object, the second object exerts a force on the first object that is equal in strength and opposite in direction. These two forces are called action and reaction forces. Both forces are exerted at the same time and either force can be considered the action force or the reaction force.

According to this law, whenever two objects interact with each other, they exert forces on each other. When you sit in a chair, your body exerts a downward force on the chair, and the chair exerts an upward force on your body. The action and reaction forces of this interaction are the force on the chair and the force on your body.

The magnitude of the force on the first object equals the magnitude of the force on the second object. The direction of the force on the first object is in the direction opposite of the force on the second object. When you hold a ball, you exert an upward force on the ball, while the ball exerts a force of equal magnitude downward on your hand.

If equal and opposite forces on an object cancel out, why don’t action and reaction forces cancel out? Forces can cancel out only if they act on the same object. Action and reaction forces do not act on the same object. When a person takes a step, the person’s foot exerts an action force on the ground. The ground, which is Earth, exerts a reaction force on the person’s foot that pushes the person forward.

1. Which is true, based on Newton’s first law? A. A ball that is in motion has a tendency to come to a stop. B. A ball that is not moving has a tendency to stay stationary. C. The net force on any moving ball is not zero. D. A force must act on a ball to prevent it from moving.
2. A pushed box is accelerating at 3.0 m/s2. If the force pushing the box is tripled, what is the acceleration of the box?
A. 0.0 m/s2 B. 1.0 m/s2 C. 3.0 m/s2 D. 9.0m/s2

### The Law of Universal Gravitation

Newton also developed the law of universal gravitation, which describes the force of gravity between any two objects that have mass. Gravity is a force of attraction between two objects because of their mass. Earth exerts gravitational force on everything on its surface. Everything on Earth’s surface exerts gravitational force on Earth. The planets, their moons, and stars exert gravitational force on one another.

Newton determined that the force of gravity depends on the masses of the objects and the distance between them. He developed an equation to identify this relationship.

In this equation, F represents the gravitational force, m1 is the mass of one object, m2 is the mass of the other object, and r is the distance between their centers. The letter G is the universal gravitational constant. Its accepted value is $G = 6.67 \times 10^{-11} N \times m^2 / kg^2$. The equation shows that the attraction between two objects gets stronger as mass increases and gets weaker as mass decreases. It also shows that gravity decreases rapidly as the distance between the objects increases.

### Weight Versus Mass

When you step on a bathroom scale, the scale measures your weight. Weight is a measure of the force of gravity on an object. Although weight depends on mass, they are not the same quantity. Mass (m) is the amount of matter in an object. Weight (W) is a force equal to the mass of an object multiplied by the acceleration due to gravity (g), W = mg.

Near Earth’s surface, the acceleration due to gravity is 9.8 m/s2 for all objects. However, the acceleration due to gravity is different on other planets because the planets have different masses. For example, the acceleration due to gravity on Jupiter is 2.6 times more than it is on Earth. So, the same object on Jupiter would weigh 2.6 times more than it would on Earth, even though the object’s mass remains the same.