Newton's Laws of Motion II

Newton's Laws of Motion II

Goals

Definitions

Forces

Free-body Diagram

A diagram that shows all of the forces on an object.

Weight

Weight is the force of the earth's gravity on an object. It is calculated by the multiplying an object's mass by g which is the gravitational acceleration at the earth's surface. We usually use g=9.8m/s2.

w=mg

Normal Force

The normal force is a contact force between two objects such as a book and a table. It is always perpendicular to the contact surfaces. There is no formula for normal force so we calculate it based on Newton's laws. See the "Choosing a Coordinate System" section for an example.

Friction

There are three types of friction we will be dealing with. They are known as static, kinetic and rolling friction. All forms of friction are proportional to the normal force on the object (kinetic and rolling are also proportional to speed, but we are ignoring this here).

Friction Type Equation Usage
Static Force must be greater than this number to accelerate from rest.
Used for stationary objects.
The less-than-equal sign means that the friction will resist only the amount of force that is applied to it up to a maximum. eg. No force means no friction.
The direction opposes the net force on the object.
Kinetic Force opposes velocity.
Always less than static friction.
Used for sliding objects.
Rolling Force opposes velocity.
Used for objects that are rolling.

Tension

Many of the problems that we will be solving will involve pulling on ropes, wires, or cables to move an object. For the most part, we will treat them as massless because we are more concerned with the motions of the objects. For the same reason we will also be using massless, frictionless pulleys. Later on, we will learn how to deal with real pulleys.

The diagram below shows the implications from above:

The tension of a massless rope is the same at all points of the rope and the tension at both sides of a massless, frictionless pulley is the same. Caution: This will not be true later in the semester when we deal with real pulleys.

Free Body Diagrams

The most important step in solving problems involving Newton's laws is drawing the free body diagram for the problem. The free body diagram allows us to see the forces interacting with each other and can give us intuition about the outcome. The following is a free body diagram of a box being pulled across the floor by a rope:

Choosing a Coordinate System

It is a good idea to align the coordinate system so that as many of the forces are parallel or perpendicular to it as possible. For instance, if we have a block sliding along an incline, it has three forces on it.

Then we divide the weight vector into its components and put a curvy line through it to indicate that it has been replaced. This makes all vectors either parallel perpendicular to the incline. A good choice for the coordinate system would be one with the x-axis along the incline.

Points to Remember

Example 1

Darlene the daring, a famous western stuntwoman, is being dragged along the ground by a rope tied to a horse. Her coefficient of kinetic friction with the ground is 1.3 and her mass is 60kg. How much force does the horse have to provide to keep Darlene moving at a constant speed?

Example 2

The system above is released from rest and accelerates. If the coefficient of kinetic friction between the block and the table is 0.5, find the tension in the string and the acceleration of the system.

Solutions