Work and Energy

Work

Force applied over distance, expends energy.

The object work is applied to gets energy called kinetic energy.

Theta is the angle between the force and the direction of motion.

If force and direction of motion are in opposite directions, the work is negative.

• Positive if in the same direction.

If F is applied at an angle to motion, then only the component of force inline with the direction of motion does any work.

If an object moves at right angled to force, no work is done.

Use the integral from x_1 to x_2 to find work done by a varying force.

Lesson 2

Energy

Is a scalar, has a magnitude but no direction.

Work

$$w = F * d * \cos{\theta}$$

Unit for work is Joules ($$N*m$$)

Use integral to find work done by a varying force.

Kinetic Energy

$$k = \frac{1}{2}mv^2$$

Net Work

$$w_{net} = \delta{k}$$

$$F * d * \cos{\theta} = \frac{1}{2}mv_f^2 - \frac{1}{2}mv_i^2$$

If speed doesn't change, kinetic energy doesn't change and no work is done.

Friction always does negative work - it points in the opposite direction of motion.

Tips

Mass and Velocity

Use kinetic energy

Force and Distance

Use work.

Conservative Forces

Conservative Force

Conserves mechanical energy.

Amount of work doesn't depend on the path taken.

Gravity

Tension

Non-Conservative Forces

Amount of work depends on the path taken.

Friction