Work and Energy

Outcomes

- Upon completion of this unit you will be able to
- Analyze force problems in terms of energy.
- Define the term "work" as it relates to physics.
- Calculate work problems using the various

equations. - Identify which forces are at work in a given

problem situation. - Interpret a force displacement curve in relation

to work. - Calculate work as done by a spring.
- Define power and efficiency.
- Calculate power and efficiency using the

appropriate formulas. - Demonstrate an understanding that power is a

product of force and velocity.

Objectives Cont

- Demonstrate an understanding of kinetic energy as

a concept and as an equation. - Calculate the change in kinetic energy using the

work-energy theorem formula. - Explain potential energy.
- Calculate gravitational potential energy.
- Define spring force.
- Calculate spring force using the formula for

Hooke's Law. - Describe conservative forces.
- Write the conservative energy statement using the

correct mathematical forms. - Solve energy problems using the appropriate

energy equations.

Work

- Work is done if a force is applied for a

particular distance. - In Physics there is one more stipulation the

force and displacement vectors must point in the

same direction. - W Fxdx
- Fx is the applied force in the direction of the

object's displacement anddx is the object's

displacement. - Why the x-subscript? This shows that in order for

work to be done, the force and displacement must

be in the same direction.

Extreme Work

- This formula for work leads us to three possible

extreme cases - Force and Displacement in the Same Direction

(results in max. positive work) - Example?

- Force Perpendicular to Displacement
- No work is done in this case
- Example?

- Force and Displacement in Opposite Directions
- this results in max. negative work
- Example?

Identify the Force at Work

- It is extremely important to identify what force

is doing the work in question. Look at the case

of lifting then lowering a box.

Lifting a box

- As you lift the box, you exert a force in the

same direction as the displacement, so you do

positive work. Gravity (weight) always acts

straight down and here that means it is in the

opposite direction to the displacement, so it

does negative work.

Lowering the box

- As the box is lowered, you still exert an upward

force to keep the box from simply falling. Now

your force and the displacement are at 180

degrees, so you do negative work. Gravity is now

doing positive work.

Units for Work

- The unit of work is the joule (J).
- lifting a good sized apple at a constant

velocity straight up for a distance of 1 m

requires about 1 J of work. - While work can be positive or negative and its

calculation depends on direction, it is not a

vector. Work is a scalar. Direction is important

for calculating work, but work itself has no

direction.

Try It

- You exert a force of 20 N in order to slide a

textbook across a table a a constant speed. If

the textbook has a mass of 20 kg and you slide it

a distance of 50 cm, How much work do you perform?

Try it Again

- A 1500 kg car is brought to a complete stop over

a distance of 43 m. If the coefficient of

friction between the car and the road is 0.32,

how much work is done by friction in bringing the

car to a stop? - Start by drawing a rough FBD of the situation

Force Displacement Graph

- Another useful fact is that the area under a

force displacement curve is equal to the work

done. Of course, the force that is plotted will

have to be the component that is in the same

direction as the displacement.

Work done on a Spring

- The work done on a spring when it is compressed

or stretched is given by the formula shown below - where k is the spring constant (N/m) and x is

the amount of compression (m). - You can not use the basic work formula W Fx for

a spring. The formula W Fx assumes that the

force is constant. As you well know, the force a

spring exerts (F) changes as the displacement (x)

changes. You must use the special formula above

if you need to calculate the work done by a

spring.

Power and Efficiency

- Power is simply the rate at which you do work.

The formula for average power is shown below. - ?W change in work (J)
- ?t change in time (s)
- The unit of power is the joule/second or the watt

(W). When you see a light bulb rated at 60 W, it

means that it consumes 60 J of electrical energy

every second.

Example

- An elevator motor lifts a mass of 1000 kg over a

distance of 20 m in 15 seconds. What power must

it develop?

- A winch rated at 1.5 kW pulls a heavy box along a

horizontal floor. It takes the winch 1.00 min to

pull the box over a distance of 250 m. What Force

is it exerting?

Power as a product of F and V

- It is possible to show that power is equal to the

force times the velocity. The formula for this is

shown below - P Fv
- F applied force (N)v object's velocity (m/s)

Efficiency

- Efficiency is the ratio of energy output to

energy input - Efficiency Eo /Ei x 100
- Eo energy output
- Ei energy input
- It can also be written as a ratio of work output

to work input - Efficiency Wo /Wi x 100
- Wo work output
- Wi work input

Example

- A toaster transforms 1200 J of electrical energy

into 560 J of thermal energy to make a piece of

toast. What is the efficiency of the toaster? - We know thatEi 1200 J Eo 560 J
- So our efficiency is