# Mechanics

calculus-based physics for scientists and engineers

## Basic Force Models in One Dimension

### Gravity Near the Surface of the Earth

This is the first of three basic force models we will use in one dimension. We will expand upon them when we move to multiple dimensions. Gravity near the surface of the earth will be called, gravity.

Our model of gravity makes the following assumptions:

1. The earth is flat and not rotating
2. $$m$$ is the mass of the object experiencing the gravitational force
3. $$g$$ is the acceleration due to gravity

With these assumptions, the magnitude and direction of the gravitational force on the object by the earth is given by:

magnitude: $$mg$$

direction: down toward the earth perpendicular to the earth's surface

### The Contact Force

The contact force describes two things with mass that are in physical contact with each other. We will want to know the force on one of them due to the other. The first is the object and the second is the agent. We would write this as the contact force on the object by the agent.

The contact force can be any magnitude and point in any direction. There are no fixed equations. You either have to be told what it is or calculate it from other information.

Thus, the magnitude and direction of the contact force on the object by the agent is given by:

magnitude: anything

direction: anywhere

### The Tension Model

For reasons that have baffled generations of physics students, problem writers have created legions of questions that involve pulling and hanging things with ropes, threads, and wires. They call the pulling force tension, but rarely explain what it is. Here we develop a well-defined model of it.

We use the tension model when we are pulling on something with a string, rope, chain, wire, etc. The string (for example) is the agent of the force. We would say there is a tension force on an object by the string. The assumptions of the model are

1. The length of the string never changes.
2. Tension only pulls, the string never pushes an object.
3. The tension between two points of contact with objects with mass is the same everywhere.

With these assumptions, the magnitude and direction of the tension force on the object by the string is given by:

magnitude: anything

direction: away from the object along the line of the string at the point of contact