Newton's Laws of Motion I

Up to now we have looked at objects in motion and how they behave, but we haven't really said how they got moving in the first place. Objects in motion were put into motion by one or more forces acting on it. When you kick a soccer ball you are exerting a force on it. Gravity is also exerting a force on the ball -- it pulls it back down to the ground. The air also exerts a force on the ball decreasing its range.

Goals

Understand Newton's three laws of motion.
Learn how to compute the net force on an object.
Use Newton's second law to determine accelerations of objects which have been acted upon by forces.

Definitions

Net Force

The sum of all the external forces acting on a body. In mathematical notation we write it as:

Superposition

This principle states that if you put several forces on an object the effect is the same as if you put their vector sum on it as a single force. Conversely, a single net force can be divided into other forces whose sum is the original force.

Summary of Newton's Laws

Newton's laws are the first real physics laws that we will encounter. They are the core of this course. You should memorize them. 1st Law
An object with constant velocity (this could be zero) will maintain that velocity (zero acceleration) unless it is acted on by some force.

This means that we must have a net force if there is an acceleration and we must have acceleration if there is a net force.

If an object, such as an astronaut, would be located far away from anything else in the universe it would stay put or, if set in motion, it would move with constant speed in a straight line. Astronauts in extravehicular activity maneuvers (EVA) are either tethered to the mother ship, or they carry small rocket propulsion devices to be able to return. The gravity pull of the space vehicle is too weak to pull back an astronaut that accidentally acquires a velocity away from the craft.

2nd Law

If an external force acts on a body it will accelerate in the direction of the force. The acceleration of the object is determined by the net force on the object divided by its mass.

The cart in the picture is acted upon by a FORCE, provided by the horse. The cart is also subject to retarding forces, such as friction and air resistance. If we add up all the forces acting on the cart we get the net force.

Forces are vectors; they have magnitude and direction. They have to be added as vectors. Newton's 2nd Law states that an object acted upon by a non-zero NET force will accelerate.

3rd Law

Every action has an equal and opposite reaction.

A force is always an interaction between two material objects.

The airplane exerts a force on the glider causing it to accelerate. The glider, in turn, exerts a force on the airplane. There are, of course, additional forces present such as the propeller force and air drag on both planes. This diagram shows the forces exerted on each plane by the other.

A Paradox?

A question that sometimes comes to mind after a beginning physics student sees Newton's laws is, "if the two objects pull on each other with the same amount of force, how does the system move?"

The answer is that there must be a net force acting on system. The force diagram from the 3rd law above is not complete, so we need to draw a complete free-body diagram for each plane.

Let's start with the airplane:

The forces are summarized in the table below:

Force	Direction
Gravity	Downward
Lift	Upward
Air Drag	Backward
Glider	Backward
Propeller	Forward

If the lift force is equal to the force of gravity then the plane does not accelerate up or down. The force of the propeller must be greater than the force of the glider plus the air drag force in order to accelerate forward.

The same procedure can be applied to the glider and we would find that the force the plane exerts on it is greater than the force of the air drag on it, so it accelerates forward with the plane.

Example 1

A 2,800,000kg rocket accelerates upward at a rate of 3.0m/s². Find the force exerted by the engines.

Hint: Don't forget gravity.

Example 2

Three dogs are fighting over a bone. One is pulling to the left with a force of 20N, another to the right with a force of 35N and the third upward with a force of 15N. What is the net force on the bone?