Work has a specific definition in physics Work has a specific definition in physics. Work is done anytime a force is applied through a distance.

W = F·d The unit is the newton•meter, or joule.

A component of the force must be in the direction of the displacement A component of the force must be in the direction of the displacement. Only this component is used when calculating the work.

Example: How much work is done on a vacuum cleaner pulled 3 Example: How much work is done on a vacuum cleaner pulled 3.0 m by a force of 50.0 N at an angle of 30.0° above the horizontal?

Work can be positive or negative depending on whether the force is in the same direction as displacement or in the opposite direction.

For example: If you push a box, the work is positive; but the work the friction does is negative.

Kinetic energy is the energy of motion. KE = 1/2 mv2

KE is a scalar and the unit is the joule.

Example: A 7. 00 kg bowling ball moves at 3. 00 m/s Example: A 7.00 kg bowling ball moves at 3.00 m/s. How much kinetic energy does the bowling ball have? How fast must a 2.45 g table tennis ball move in order to have the same kinetic energy as the bowling ball? Is this reasonable?

The net work done by a net force acting on an object is equal to the change in the kinetic energy of the object.

This is called the work-kinetic energy theorem: W = ΔKE

Example: 25 joules of work is done to a 2 kg ball Example: 25 joules of work is done to a 2 kg ball. If the ball is not moving initially, how fast is it moving after the work is done?

Example: A person kicks a 10 Example: A person kicks a 10.0 kg sled, giving it an initial speed of 2.2 m/s. How far does the sled move if the coefficient of kinetic friction between the sled and the ice is 0.10?

Potential Energy is stored energy, energy of possible motion, energy of position.

One type of potential energy is gravitational potential energy One type of potential energy is gravitational potential energy. PE = mgh

Example: A 5 kg bunch of bananas is at the top of a 6 meter palm tree Example: A 5 kg bunch of bananas is at the top of a 6 meter palm tree. What is the gravitational potential energy of the bunch of bananas?

PE = mgh is just W = Fd.

The unit of potential energy is the joule The unit of potential energy is the joule. (The unit of all types of energy and work is the joule.) It is always measured relative to a zero level.

Another type of potential energy is Elastic Potential Energy Another type of potential energy is Elastic Potential Energy. This energy is stored in a compressed or stretched object.

The formula for elastic potential energy is: PEelastic = 1/2 kx2 The symbol k is the spring constant, x is the distance compressed or stretched.

The spring constant is a measure of the force needed to stretch or compress a spring. It is measured in newtons per meter, N/m.

Example: How much energy is stored in a spring with a spring constant of 10 N/m if it is stretched 2 meters?

Example: A 70.0 kg stuntman is attached to a bungee cord with an unstretched length of 15.0 m. He jumps from a height of 50.0 m. When he stops, the cord has stretched to 44. 0 m. If k for the cord is 71.8 N/m, what is the total PE relative to the ground when the man stops falling?

When we say something is conserved, we mean it remains constant.

Mass is a conserved quantity.

The motion of many objects involves a combination of potential and kinetic energy.

The two types of potential energy (gravitational and elastic) plus kinetic energy form a quantity called mechanical energy.

ME = KE + ΣPE The other types of energy form nonmechanical energy.

Mechanical energy is often conserved. MEi = MEf

An example of this is a pendulum.

Example: A diver steps off the edge of a platform that is 10-m above the water. What is his velocity when he hits the water?

Example: If the diver weighs 500 Newtons, what is his kinetic energy when he hits the water?

Example: What is the potential energy of the 500 N diver while on the 10 m platform?

Example: Compare the two answers Example: Compare the two answers. Can you make some sense of the results?

MEi = MEf This is only true if there is no friction.

MEi = MEf 1/2 mv2i + mghi = 1/2 mv2f + mghf

Example: Starting from rest, a child slides down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Her mass is 25.0 kg. How should we do this problem?

If the slope if this slide were constant, we could use the kinematic equations to solve this problem.

But, we don't know the slope, or if it is constant (acceleration may not be constant).

But, comparing energy is not affected by the shape of the path, so we don't need the slope. We just remember that MEi = MEf.

Example: Starting from rest, a child slides down a frictionless slide from an initial height of 3.00 m. What is her speed at the bottom of the slide? Her mass is 25.0 kg.

Mechanical energy is not conserved in the presence of friction Mechanical energy is not conserved in the presence of friction. (Total energy is conserved, but not mechanical.)

Power is the rate at which work is done. P = W/Δt

Since W = Fd and P = Fd/t and d/t = v, P = Fv is also true.

The SI unit of power is the watt, which is equal to one joule per second.

Machines with different power ratings do the same work in different time intervals.

Example: Superman is "more powerful than a speeding locomotive Example: Superman is "more powerful than a speeding locomotive." What does this mean?

Example: A 193 kg curtain needs to be raised 7 Example: A 193 kg curtain needs to be raised 7.5 m, at a constant speed, in a time as close to 5.0 s as possible. The power ratings for three motors are 1.0 kW, 3.5 kW, and 5.5 kW. Which motor is best?