Work, Energy and Power

-In the previous units/chapters, we utilized Newton's laws to analyze the motion of objects.

-In this unit, motion will be approached from the perspective of work and energy. The effect that work has upon the energy of an object (or system of objects) will be investigated; the resulting velocity and/or height of the object can then be predicted from energy information.

Work• A force acting upon an object to cause a

displacement. - three key words - 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.

• Mathematically,

where F = force, d = displacement, and the angle (theta) is defined as the angle between the force and the displacement vector.

Three scenarios. Give examples

Scenario A:

Scenario B:

Scenario C:

Read the following statements and determine whether or not they represent examples of work.

1. A student applies a force to a wall and becomes exhausted.

No.This is not an example of work. The wall is not displaced. A force must cause a displacement in order for work to be done.

2. A book falls off a table and free falls to the ground.

Yes. This is an example of work. There is a force (gravity) which acts on the book which causes it to be displaced in a downward direction (i.e., "fall").

Examples 3. A waiter carries a tray full of meals above his head

by one arm straight across the room at constant speed.

No. This is not an example of work. There is a force (the waiter pushes up on the tray) and there is a displacement (the tray is moved horizontally across the room). Yet the force does not cause the displacement. To cause a displacement, there must be a component of force in the direction of the displacement.

Examples

4. A rocket accelerates through space.

Yes. This is an example of work. There is a force (the expelled gases push on the rocket) which cause the rocket to be displaced through space.

What about this?• A chain pulling upwards and rightwards upon

Fido in order to drag Fido to the right. It is only the horizontal component of the tensional force in the chain which causes Fido to be displaced to the right.

Work is the transfer of energy.

• In physics we say that work is done on an object when we transfer energy to that object.

• If you put energy into an object, then you do work on that object.

• If a first object is the agent that gives energy to a second object, then the first object does work on the second object. The energy goes from the first object into the second object. At first we will say that if an object is standing still, and you get it moving, then you have put energy into that object.

Example• A golfer uses a club and gets a stationary golf ball moving when he or

she hits the ball. The club does work on the golf ball as it strikes the ball. Energy leaves the club and enters the ball. This is a transfer of energy. Thus, we say that the club did work on the ball.

• And, before the ball was struck, the golfer did work on the club. The club was initially standing still, and the golfer got it moving when he or she swung the club.

Conclusion

• So, the golfer does work on the club, transferring energy into the club, making it move. The club does work on the ball, transferring energy into the ball, getting it moving.

Energy transfer

Work is a kind of energy transfer.When a force moves something the

energy transfer is called work.• Work isn't a form of energy - it's one of the ways

that energy can be transferred. • The amount of work done is the same as the

amount of energy transferred. • The amount of work is measured in joules (J). • The distance is measured in the direction of the

force.

work = force x distance moved

Example

Q.By dragging a sledge up a slope, how much work are you doing against friction?

Work = size of frictional force x distance moved in direction of frictional force= 40N x 100m= 4,000 JWhere did this 4 000 J come from and where did it go?

Energy Types

Since energy comes in so many forms and, as we will see, is also constantly changing from one form into another, selecting a perfect set of 10 basic types is not easy.

Types of Energy In science, we say that energy is the

ability to do work.

We need energy to do all the things we do.

• Reading a book needs energy.  

• Running needs energy. 

• Riding a bicycle needs energy. 

• Watching TV needs energy.   

Even sleeping needs energy. 

Everything that happens in the world involves movement and for something to move, energy is required.

If something takes energy in, then it also gives energy out.

A light bulb can get energy from the mains electricity supply.

The bulb gives energy back as light and as heat. 

Examples

• A person riding a bicycle gets their energy from the food they eat.  

• Energy is given out as  sound and as heat. 

Work Concepts

Energy Concepts

Potential Energy • An object can store energy as the result of its

position.

• For example, the heavy ram of a pile driver is storing energy when it is held at an elevated position. This stored energy of position is referred to as potential energy.

Example

• A drawn bow is able to store energy as the result of its position. When assuming its usual position (i.e., when not drawn), there is no energy stored in the bow. Yet when its position is altered from its usual equilibrium position, the bow is able to store energy by virtue of its position. This stored energy of position is referred to as potential energy.

Potential energy is the stored energy of position possessed by an object.

Two forms of potential energy 1. Gravitational potential energy

The energy stored in an object as the result of its vertical position (i.e., height). The energy is stored as the result of the gravitational attraction of the Earth for the object. The gravitational potential energy of the heavy ram of a pile driver is dependent on two variables - the mass of the ram and the height to which it is raised. There is a direct relation between gravitational potential energy and the mass of an object; more massive objects have greater gravitational potential energy. There is also a direct relation between gravitational potential energy and the height of an object; the higher that an object is elevated, the greater the gravitational potential energy. These relationships are expressed by the following equation:

PEgrav = mass * g * heightPEgrav = m * g * h

How to determine the GPE?To determine the gravitational potential energy

of an object, a zero height position must first be arbitrarily assigned. Typically, the ground is considered to be a position of zero height.

Try this example• Since the gravitational potential energy of an

object is directly proportional to its height above the zero position, a doubling of the height will result in a doubling of the gravitational potential energy. A tripling of the height will result in a tripling of the gravitational potential energy. Knowing that the potential energy at the top of the tall pillar is 30 J, what is the potential energy at the other positions shown on the hill and the stairs.

Are you ready?

Check your understanding• A cart is loaded with a brick and pulled at

constant speed along an inclined plane to the height of a seat-top. If the mass of the loaded cart is 3.0 kg and the height of the seat top is 0.45 meters, then what is the potential energy of the loaded cart at the height of the seat-top?

P.E = m*g*h = (3.0kg)*(9.8m/s2)*(0.45m)

Translational kinetic energy The energy of motion. An object which has motion -

whether it be vertical or horizontal motion - has kinetic energy. The amount of translational kinetic energy which an object has depends upon two variables: the mass (m) of the object and the speed (v) of the object.

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. The kinetic energy is dependent upon the square of the speed.

Check Your Understanding Q.1 Determine the kinetic energy of a 1000-kg

roller coaster car that is moving with a speed of 20.0 m/s. K.E = (½)(1000-kg)(20.0m/s)2 = 200 000 Joules

Q.2 If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy?If the speed is doubled, then the K.E is

quadrupled.Thus, K.E = 4 (200 000 Joules) = 800 000

Joules

ExamplesQ.3 A 750-kg compact car moving at 100

km/hr has approximately 290 000 Joules of kinetic energy. What is the kinetic energy of the same car if it is moving at 50 km/hr?

The K.E is directly related to the square of the speed. If the speed is reduced by a factor of 2 (as in from 100 km/h to 50 km/h) then the K.E will be reduced by a factor of 4. Thus, the new KE is (290 000 J/4) or 72 500 J

The Law of Conservation of EnergyEnergy in a system may take on various forms (e.g.

kinetic, potential, heat, light). The law of conservation of energy states that energy may neither be created nor destroyed. Therefore the sum of all the energies in the system is a constant.

Pendulum:• mass, m = 1kg

height, h = 0.2 m gravity, g = 9.8 m/s2

• PE = mgh PE = 1.96J

Check your knowledge• Describe the position of BLUE BALL.

The position of the blue ball is where the Potential Energy (PE) = 1.96J while the Kinetic Energy (KE) = 0. As the blue ball is approching the purple ball position the PE is decreasing while the KE is increasing. At exactly halfway between the blue and purple ball position the

PE = KE.

Describe the position of PURPLE BALL.

The position of the purple ball is where the Kinetic Energy is at its maximum while the Potential Energy (PE) = 0. At this point, theoretically, all the PE has transformed into KE> Therefore now the KE = 1.96J while the PE = 0.

Describe the position of PINK BALL.

The position of the pink ball is where the Potential Energy (PE) is once again at its maximum and the Kinetic Energy (KE) = 0.

The sum of PE and KE is the total mechanical energy:

Total Mechanical Energy = PE + KE

Energy Transformation for a Pendulum

Energy Conservation on an Incline

How High Will It Go?

A Roller Coaster is waiting for you!

Energy Transformation on a Roller Coaster