Work, Power, and Energy

In physics, work is defined as a force acting upon an object to cause a displacement. There are three key words in this definition - force, displacement, and cause. In order for a force to qualify as having done work on an object, there must be a displacement and the force must cause the displacement. The displacement must be in the same direction as the force.

Mathematically, Work = Force x displacementAs long as the displacement is in the same direction as the force, the displacement can be changed to distance.

Work = Force x distanceW = Fd

Is work being done on the cart being dragged up the hill?

Is work being done on the wheelchair?

If the car is not moving, does the person pushing do work on the car? He looks exhausted.

Is the waiter doing work on the tray?

An object with a mass of 15 kg is being pushed by a 100 N force for a distance of 5 meters. How much work is being done on the object?

W = FdW = 100 N x 5 meters = 500 N∙mOr 500 Joules or 500 J

A student with a mass of 80.0 kg runs up three flights of stairs in 12.0 sec. The student has gone a vertical distance of 8.0 m. Determine the amount of work done by the student to elevate his body to this height. Assume that her speed is constant.

Answer on next slide

The force in this case is the student’s weight. Weight = mg

Weight = 80 kg x 10 m/sec2 Weight = 800 N Work = Force x distanceWork = 800 N x 8.0 m Work = 6400 J or 6.4 kJ

The quantity work has to do with a force causing a displacement. Work has nothing to do with the amount of time that this force acts to cause the displacement. Consider this scenario: Two neighbors mow identical lawns with identical lawn mowers using the same amount of force on each mower.

Say both neighbors mow 100 meters of lawn while applying 50 N of force to the mower. Which means both neighbors do 5000 J of work. Neighbor #1 completes the job in 10 minutes; neighbor #2 completes the job in 20 minutes.

The difference between the two neighbors is the rate at which they did the work.

A rate is something over time.

Examples of rates are: speed, and acceleration. Speed compares the distance traveled over time. Acceleration compares how the velocity changes over time.

The rate which compares the amount of work over time is called power.

The neighbor who mowed the lawn in 10 minutes did the same work but in less time; therefore, he did the job with more power.

Mathematically:

Power = Work timeWork is measured in Joules, time in

seconds. The unit of power is Joule/sec which is called a watt. 746 watts is equivalent to 1 horsepower(hp.).

How much power is developed if you lift a 100 kg rock a distance of 10 m in 5 seconds?

When an object is being lifted the force is the object’s weight. The weight of a 100 kg rock is 1000 N. Weight = mass x g

Power = Work ÷ timePower = (1000 N x 10 m) ÷ 5 secPower = 2000 W or 2 kW

Imagine a student can go up a 1.5-m stairwell in 2 s. If he weighs about 900 N(200 lbs.), how much power does he develop going up the stairs?

Plug into the equation:Force = 900 NDisplacement = 1.5 mTime = 2 sPower = Work ÷ timePower = (Force • distance) ÷ timePower = (900 N • 1.5 m) ÷ 2 sPower = 1350 J ÷ 2 sPower = 675 watts675 watts is approximately .9 hp.

Historically, power ratings are given to machines to represent the amount of work they deliver over a unit of time.

The Bugatti Veyron® claims a world record, horsepower rating of 987 hp. Which means the engine does 736 kJ of work every second. By comparison the McClaren F1, the former record holder, is 514 hp. That’s 383 kJ of work every second.

Mechanical energy is the energy which is possessed by an object due to its motion or from its position in space. Mechanical energy comes in two forms: potential & kinetic.

Potential energy is the energy an object has due to its position. If the position refers to the object’s height the stored energy is called gravitational potential energy.

When the position refers to the distance an object has been stretched or compressed like a bowstring or spring, the energy is called elastic potential energy.

This stretched spring has elastic potential energy stored in it.

Gravitational potential energy depends on two factors: mass and height. As stated previously, the higher an object’s position, the greater its gravitational potential energy(GPE). The GPE is equal to the object’s height times its weight.

GPE = weight x height. The weight is also mass x g, so we can

rewrite the equation as:GPE = mass x g x height

GPE = mgh

To determine GPE you must first establish a reference point. Usually, it’s the ground or the earth’s surface. However, it could be a tabletop or any surface point. It depends which is most convenient.

Which is the reference point, the floor or the chair?

It depends on your choice, it could be either.

GPE is proportional to the height regardless of how it reached that height. It doesn’t matter whether the ball is lifted straight up, rolled uphill, or moved up stairs. The GPE remains the same for that height.

Kinetic energy is the energy of motion. An object which has motion - whether it be vertical or horizontal motion - has kinetic energy. The amount kinetic energy which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object. The following equation is used to represent the kinetic energy (KE) of an object:

KE = ½ m v2

KE is kinetic energy, m is the mass, v is the speed. This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed. That means that for a twofold increase in speed, the kinetic energy will increase by a factor of four; for a threefold increase in speed, the kinetic energy will increase by a factor of nine; and for a fourfold increase in speed, the kinetic energy will increase by a factor of sixteen. Kinetic energy is a scalar quantity; it does not have a direction.

Mechanical energy is the energy which is possessed by an object due to its motion or its stored energy of position. Mechanical energy is the sum of both the kinetic and potential energy possessed by the object. An object that has mechanical energy has the ability to do work.

The total amount of mechanical energy is merely the sum of the potential energy and the kinetic energy. This sum is simply referred to as the total mechanical energy (abbreviated TME).

TME = PE + KE

Notice also that the total mechanical energy of the skier is a constant value throughout her motion. She begins with 50000 J of PE and the sum of the PE and KE remains 50000 J regardless of the skier’s position.

A simple machine is a device that does work for you. You still must do work to a machine to get work out of a machine. A simple machine either multiplies or changes the direction of a force or both. So even though you have to do work to a machine, it makes the work easier. It is impossible to get more work out of a machine than you put into a machine. If a machine were frictionless the work output would be equal to the work input of a machine.

There are four basic types of simple machines: pulley, lever, inclined plane, and wheel and axle. A pulley is a device used to lift heavy objects a great distance. A pulley is a device used to lift heavy objects a great distance. A fixed pulley is usually a wheel with a cord. Multiple pulleys can be used to reduce the input force; however the overall output work is still less than input.

The amount that a machine reduces the input force is called the mechanical advantage(MA). The mechanical advantage is the output force divided by the input force. A single fixed pulley has a MA of 1 because it does not multiply a force. A single movable pulley has an MA of 2 which means one can lift 1000 N with only 500 N of input force.

A lever is a type of simple machine typically used to lift heavy objects small distances. The principle of levers was discovered by the ancient Greek physicist Archimedes in the third century B. C. Usually, a lever is a straight object which pivots on a point called a fulcrum.

fulcrum

A seesaw is an example of a first-class lever. The fulcrum is between the input and output forces.

Force

Force

fulcrum

Is a pair of scissors a first class lever?

fulcrum

Input force

Output force

Yes!

In a second class lever the output force (weight being lifted) is between the fulcrum and the input force. A typical example of a second class lever is a wheelbarrow.

The wheel is fulcrum. The barrow is where you put the load to be lifted. The input force is at the other end.

fulcrum

In a third class lever the output force is at the opposite end of the fulcrum. The human arm is a third class lever with the fulcrum at the shoulder joint. Anything that acts as an extension to the arm is also a third class lever like a hammer or a baseball bat.