Work and Energy

1
Work and Energy
2
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.

3
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.

4
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.

5
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?

6

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

7

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

8
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.

9
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.

10
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.

11
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.

12
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?

13
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

14
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.

15
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.

16
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.

17
Example

• An elevator motor lifts a mass of 1000 kg over a
  distance of 20 m in 15 seconds. What power must
  it develop?

18

• 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?

19
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)

20
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

21
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