Work, Energy, and PowerWork, Energy, and Power

What are the forms of energy?•Heat•Chemical•Nuclear•Light(Solar)•Mechanical•Electromagnetic Energy

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.

The higher up this ladder you climb the greater your 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 heightGPE = 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.

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.

Consider these three situations:A teacher applies a force to a wall and becomes exhausted.Does the teacher do work on the wall?No, even though a force is applied, the wall does not move. No displacement, no work!

A book falls off a table and free falls to the ground. Is work done on the book?

To determine if work is being done, there are three questions to answer. First, is the book moving?

Yes, a falling book is definitely moving.

Second, is there a force acting on the book?

Yes, The book’s weight is the force.

The third question is: Does the force cause the motion?

Yes, the book’s weight is pulling the book down, and the book is falling down.

The answer is yes to all three questions; therefore, work is done on the book by its weight.

Consider this situation: A waiter carries a full tray above his head by one arm across the restaurant. Does the waiter’s arm do work on the tray?

Consider the following picture:Consider the following picture:

Let us answer the three questions. Is the tray moving?

Yes, the tray is being carried across the room.

Does the waiter’s arm exert a force on the tray?

Yes, the waiter’s arm is holding the tray up; otherwise, the tray would have fallen to the floor.

Does the force cause the motion?

The answer is NO!!!

The waiter’s arm is ONLY holding up the tray. It is exerting a force which cancels out the tray’s weight, preventing the tray from falling. The tray is moving HORIZONTALLY. The waiter’s arm is NOT causing that. The waiter’s arm is NOT doing work on the tray.

The equation for work is as follows:

`W = F x dW = work, F = force, d = displacementForce is measured in Newtons, displacement is measured in meters. Work is measured in N•m or Joules.

Consider this problem: A 100 N force is applied to a 15 kg object to move it 5 m at a constant velocity.

100 N

W = F x dW = 100 N x 5 m = 500 N•m = 500 JThe mass of the object doesn’t matter. Only the force on the object, and how far it moved.

15 kg

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.

Neighbor #1 completes the job in 10 minutes; neighbor #2 completes the job in 20 minutes. Both neighbors used the same force over the same displacement; therefore they did the same amount of work. What is the difference?

The difference 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. 750 watts is equivalent to 1 horsepower(hp.).

Historically, power ratings are given to machines to represent the amount of work they deliver over a unit of time. Suppose that a 40-hp. engine could accelerate the car from 0 to 60 mi/hr in 8s. If this were the case, then a car with four times the horsepower could do the same amount of work in one-fourth the time.

That is, a 160-hp. engine could accelerate the same car from 0 to 60 mi/hr in 2 s.

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 • displacement) ÷ timePower = (900 N • 1.5 m) ÷ 2 sPower = 1350 J ÷ 2 sPower = 675 watts675 watts is approximately .9 hp.

Kinetic energy is the energy of motion. An object which has motion - whether it be vertical or horizontal motion - has kinetic energy. The amount of 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 = ½mv2

This equation reveals that the kinetic energy of an object is directly proportional to the square of its speed.

This means that if you double the velocity the kinetic energy is increased by a factor of 4. This is because the velocity is squared. If you triple the velocity the kinetic energy is increased by a factor of 9. If you decrease the velocity by 1/3rd then the kinetic energy is decreased by a factor of 1/9th. Bonus question: By what factor must you increase the velocity to double the kinetic energy?

The answer is √2, about 1.41, because √22 = 2

What is the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18 m/s? KE = ½mv2 KE = ½(625 kg)(18 m/s)2

KE = ½(625)(324)KE = 101,250 Joules

Missy Diwater, the former platform diver for the Ringling Brother's Circus, had a kinetic energy of 12 000 J just prior to hitting the bucket of water. If Missy's mass is 40 kg, then what is her speed?

12 000 J = ½ * (40 kg) * v2

300 J = ½ * v2

600 J = v2

v = 24.5 m/s

An object which possesses mechanical energy is able to do work. In fact, mechanical energy is often defined as the ability to do work. Mechanical energy enables an object to apply a force to another object in order to cause it to be displaced. The total mechanical energy is the sum of the kinetic and potential energy.

ME = PE + KE