What is Energy?

Energy comes in many forms, kinetic, potential (stored), heat, etc. Energy is always conserved. It is not created or destroyed but is just transformed from one form to another. Newton's laws relate to energy as Energy = FORCE * DISTANCE

Similarly, a force can be described as the time rate of change of momentum of an object (see below).

In every day life a lot of energy is dissipated as heat due to friction.

Let's do the experiment with friction turned on:

Notice that the smallest force can barely move the mass and that it can't move the pyramid at all. This is because its force is insufficient to overcome the frictional forces between the pyramid and the ground.

In this simulation, even when the big force pushes the pyramid its motion rapidly damps out; most of the energy is dissipated as heat.

Frictional forces depend upon the total force which is directed perpendicular to the surface. The more weight per unit area, the larger the frictional force.

Here is a more complete description of friction.

Kinetic and Potential Energy:

Throwing a ball into the air represents a situation in which the total energy is fixed and there is a continous transformation from kinetic energy to potential energy.

- When the ball is on the ground there and not moving there is no potential energy or kinetic energy
- when the the ball is tossed into the air it will reach a maximum height which is determined by how much kinetic energy it has (air resistance is important however)
- when the ball reaches its maximum height its velocity is 0 and all of the energy in the system is potential energy
- as the ball falls to the ground that potential energy is converted to kinetic energy

Kinetic Energy = Energy Associated with Motion

1/2 mass * Velocity * Velocity = 1/2mv^{2}

Momentum is Mass * Velocity = mv

Conservation of Momentum is a rule of mechanics. your intution has already told you about it.

Consider hitting a baseball. The bat, with some mv, makes
impulsive contact with a ball - m_{bat} is greater than
m_{ball} and since:

then v_{ball} is greater than
v_{bat} (provided that you hit the ball and not just air).

Same principle holds in the situation of cannon recoil:

Potential Energy --> object has a position in a force field

Potential Energy = mass * grav. acceleration * height

PE = mgh

g = gravitational acceleration of the earth

since F = ma and since the earth exerts a continuous gravitational force on all objects of mass, m, then the manifest force is

F = mg --> this is what weight is !

Now look what Newton says we can now do