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Work, Energy and Power

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W = Fs

- W= work
- F = force
- s = displacement
- Whe a force makes an object move, work has been done.
- Whenever work is done, energy is transferred form one place to another or transformed from one form to another.
- Units are = 1Nm = 1J(joule)

- A 150N force moves an object through a displacement of 6m. Calculate the work done.

- Answer: W=Fs=150 x 6 = 900J

- Work isn’t always done in a stratight line. That means we have to take into account the direction of the displacement. This is done by adding “cosθ” to the equation.
- W = F s cosθ
- This means that work done is only in the same direction of the force vector.

- A force F = 100N is used to move a box though a horizontal distance of 14m. If the force is applied to the box at angle θ = 35° as shown, calculate the work done on the box.

- Answer: 1147J

- This equation is only applicable if the force is constant.
- In real life there are lots of non-constant forces.
- We can use a graph to determine work done.
- On a Force/Displacement graph the area under the graph is the work done.

There are lots of different forms of energy.

- Kinetic
- Gravitational potential
- Elastic potential
- Electrical potential
- Light(radiation)
- Nuclear(mass)
- Chemical potential
- Sound
- Thermal

- Ek of an object is numerically equal to the work done.
- Associated with objects in motion
- Depends on both an objects
speed and mass

- It is a scalar quantity

- Kinetic energy = 1/2 *mass*speed2
- Ek = W = 1/2 mv2
- The unit of KE is joule(J)
- If the speed is doubled the energy is quadrupled.
- Ek can also be defined in terms of the momentum of an object.
- Ek = p2 / 2m

- A bowling ball and a volleyball roll at the same speed.
- Which has more kinetic energy?

- A 7kg bowling ball moves at 3 m/s. How fast must a 2.45 g ping pong ball move to have the same kinetic energy as the bowling ball?
- KE=1/2 mv2

Practice Problems:

- Determine the kinetic energy of a 625-kg roller coaster car that is moving with a speed of 18.3 m/s.
- If the roller coaster car in the above problem were moving with twice the speed, then what would be its new kinetic energy?
- 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?
- A 900-kg compact car moving at 60 mi/hr has approximately 320 000 Joules of kinetic energy. Estimate its new kinetic energy if it is moving at 30 mi/hr. (HINT: use the kinetic energy equation as a "guide to thinking.")

Answers:

- 105,000J
- 419,000J
- 24.5m/s
- 80,000J

- Calculate the kinetic energy of a 110kg rugby player running the 100m in time 15s.

- Answer: Vavg = Δs/Δt = 100/15 = 6.67m/s
- Ek = ½ mv2 = 0.5 x 110 x 6.672
- Ek = 2440J

- Calculate the momentum of the rugby player in the previous example using Ek = p2 / 2m

- Answer:
- Ek = p2 / 2m

- Associated with an object that has the potential to move because of its position
- Depends on the interaction with its environment
- store energy as the
result of its position

- Gravitational potential energy
- Potential energy due to gravity

- the energy stored in an object as the result of its vertical position or height.
- ΔEp = mass*free-fall acceleration*height
- ΔEp = mgΔh

- ΔEp = mgΔh
- Notice that ΔEpis dependant on free-fall acceleration being constant.
- Also notice that g and h aren’t properties of the actual object.

- ΔEp = mgΔh
- The higher that an object is elevated, the greater the gravitational potential energy
- a doubling of the height will result in a doubling of the gravitational potential energy

- Is it possible to have a negative potential energy?
- Can an object have both a positive potential energy and a negative potential energy?

- How is h defined?
- Relative to a “zero”

- What can be a “zero”?
- Anything can be defined as “zero”

- Discussion: A ball that falls from one building rooftop to another buildings rooftop. Where is zero?

- Calculate the gain in potential energy of a 70kg person climbing 5 flights of stairs through a vertical height of 20m.

- Answer:
- ΔEp = mgΔh = 70 x 10 x 20 = 14000J

- Energy cannot be created or destroyed. I simply changes from one form to another.
- Ebefore = Eafter
- Ek = Ep
- ½ mv2 = mgh

- An object falls from a height of 25m. Calculate its velocity as it hits the ground.
- Use energy conservation, not the 4K equations.
- Ebefore = Eafter
- Ek = Ep
- ½ mv2 = mgh

- Answer:
- v2 = 2gh = (2 x 10 x 25)
- v = 22.4m/s

At a railway station, two trains slowly collide in order to “couple” (join together). If one train of mass 12000kg is moving at 0.75m/s and the other of mass 3000kg is stationary, calculate the velocity of the two as they move away.

We already solved this for .6m/s. Now tell me the kinetic energies before and after the collision.

- A boy of mass 30 kg is being given a lift on the back of a 10kg bicycle by a girl of mass 40kg. They are travelling at a steady speed of 2.5m/s.
- The boy wishes to get off the back of the bicycle while it is still moving.
- (PART A)He knows that if he just puts his feet on the ground and stands up he is likely to fall over. Explain why.
- So instead he pushes himself off the back of the bicycle by pushing forward on the bicycle frame with his hands, so that he lands on the ground with zero horizontal velocity.
- (PART B) Calculate the velocity of the bicycle and the girl immediately after the boy has left the bicycle.
- (PART C) Calculate the total kinetic energy of the system (bicycle and both children) before and after the boy gets off. Explain the reason for any difference.

Answer:

PART A: His feet will stop when they hit the ground but his body will still be travelling forward at the bike speed, so he will fall over forwards.

PART B: 4m/s

PART C: before – 250J

after – 400J

The increase in KE is due to energy provided or work done by the boy pushing on the bicycle.

- is the rate at which work is done
- or the rate at which energy is consumed
- P = W/t
So….

- The more power you have the more work you can do in the same time.
- The more power you have you can do the same amount of work in a shorter time.
- There is an inverse relationship between work and power

Remember: P = W/t

Quick review: what is work?

- W = Fd
Quick review: what is velocity?

- v = Δx/Δt or v = d/t
- So P = F (d/t)
- Or P = F v

- P = F v
- This equation shows us that a powerful machine is both strong (big force) and fast (big velocity).
- Ex. A powerful car engine is strong and fast.

- Equations for power are:
- P = W/t
- P = F (d/t)
- P = F v
- P = ΔE/t

The SI unit of power is the watt.

- 1 watt is = 1 joule / second
- W = J / s

Horsepower is also a unit.

- 1 horsepower = 746 watts
- Hp = 746W

- A dim light bulb 40 W
- A really bright bulb 500 W
- Indoor Christmas light .7 W
- Outdoor Christmas light 7 W

- A 193kg curtain needs to be raised 7.5m, in 5s. You have 3 motors with power ratings 1.0kW, 3.5kW and 5.5kW. Which motor is best for the job?
- How much time would it take for each motor to do the same amount of work?

- Two horses pull a cart. Each exerts a force of 250.0 N at a speed of 2.0 m/s for 10.0 min.
- 1) What is the power delivered by the horses?
- 2) How much work is done by the two horses?

Practice:

- Two physics students, Will N. Andable and Ben Pumpiniron, are in the weightlifting room. Will lifts the 100-pound barbell over his head 10 times in one minute; Ben lifts the 100-pound barbell over his head 10 times in 10 seconds. Which student does the most work? Which student delivers the most power?
- During a physics lab, Jack and Jill ran up a hill. Jack is twice as massive as Jill; yet Jill ascends the same distance in half the time. Who did the most work? Who delivered the most power? (plug in fake numbers)
- When doing a chin-up, a physics student lifts her 42.0-kg body a distance of 0.25 meters in 2 seconds. What is the power delivered by the student's biceps?
- Mr. B gets bored after school one day and decides to play in the hall. He sits in his rolling chair and pushes off the wall with 12N of force producing 30W of power. What was his resulting speed he traveled down the hallway?

- Calculate the power generated in the legs of a 60kg student climbing a flight of stairs through a vertical height of 8m in a time of:
- 1.2sb) 0.75s
- *Hint: Think energy change.

- Answer:
- A) Power = W/t = mgh/t = (60*10*8)/1.2 = 4000W B) Power = W/t = mgh/t = (60*10*8)/0.75 = 6400W

- Pg 112 #2, 3, 4, 6, 10, 11, 13-16