Warmup

A marble with a mass of .002 kg and a velocity of 2m/s hits another stationary marble of equal mass. After the elastic collision, they have equal forward velocities and exactly opposite 0.5 m/s sideways speeds.

What is the forward velocity component after the collision?What is their overall velocity?

WarmupChoose either:

A person pushes a 1000 kg car sideways along flat ground with a force of 4000 N for a distance of 100 m. Then, without being pushed, the car rolls up a hill. How high up the hill does it get before coming to a stop?

Simplify:

2x -2*(3-x)=0

5x^2 + 2y = zwhere x=4, y=-1solve for z

3/x + 2 = -3

Answers: 40 meters, x=3/2, z=78, x=-3/5

Opening Activity

1) An engine piston moves forwards 1 m with a force of 100N . Then it moves backwards 1 m with a force of 25 N. How much work is done per cycle? If the engine is moving at 1500 rpm (rotations per minute), how many Watts is it producing?

2) An engine does 15,000 J of work on a motorcycle, which has a mass of 150 kg. Assuming it started at 0 m/s, how fast is the motorcycle now moving?

Energy, Work, and Power

Wednesday, November 9th, 2011

Note-taking Preview

Energy is the ability to cause change, and is measured in Joules (J).

Law of Conservation of Energy - Energy can be transferred from object to object, and can change form, but never just disappears.

Kinetic Energy – Large-scale motion. (Joules)KE = ½ m v2

Potential Energy – Based on position and a force. (Joules)PE = m g h

Work – A transfer of one kind of energy to another. (Joules)W = F d

Power – How quickly the work is done. (Watts)P = W/t

WORK (DEFINITION)

W = F * d

Work is the application of force over a distance.

What work is not:Pushing on something stationary.Pushing on something in a direction perpendicular to the direction it is moving.

WORK (POSITIVE VS NEGATIVE)Work is measured in Joules (J), just like energy. An object which does work loses energy. An object which has work done to it gains energy.

You need to consider whether the change in energy is positive or negative.

Example:A car engine does 1000J of work on a car. The car has gained 1000J of kinetic energy. The engine has lost 1000J of heat energy. Overall energy is conserved.

A weight lifter exerts a force on the weights over some distance, doing work to it. The weights have been lifted up, gaining potential energy. The weight lifter has burnt some calories (also a unit of energy, by the way) losing chemical energy.

1) A hydro-electric dam has water fall through a turbine to generate electricity. Find the force of gravity on 1 kg of water. How many joules would this produce if the turbine is pulled 10 meters at a time?

1 2 3 4 5 6

0%

8%

0%0%

92%

0%

1. 100 W2. 1000 W3. 10 W4. 100 J5. 1000 J6. 10 J

2) A person on a bicycle has a downward force of 1000 N. They coast 2500 m along a flat road. How much work is done?

1 2 3 4 5

75%

17%

8%

0%0%

1. 2500000 J2. 2.5 J3. 1500 N4. 3500 J5. None of the

above

Power (Definition)

P = W / t

Power is a measure of how quickly work is done.

It’s units are Watts, which are made of Joules/second. You’ve already heard light-bulbs described in Watts. A bigger number means it uses up more energy every second (and is usually correspondingly brighter).

When we say something is more powerful, we mean that it can do more work in the same amount of time than something else.

3) A lightbulb uses 60W. A battery stores 6000 J. For how many seconds can the battery power the lightbulb?

1 2 3 4 5

67%

33%

0%0%0%

1. 360000 s2. 100 s3. 1000 s4. Cannot be

determined5. None of the

above

4) A motor boat’s engine uses 5,000 J of energy in only 4 seconds. How powerful is it?

1 2 3 4 5

0%

91%

9%

0%0%

1. 20,000 W2. 1250 W3. 5004 W4. 4996 W5. None of the

above

Potential Energy

Definition: Energy based on the location of mass within a force field.

Equation: PE = m * g * hPE is Potential

Energym is massg is gravity*h is height*

*Most of our problems will deal with gravity, and the height above the floor.

Other Common Sources of Potential Energy•Compression (springs)•Tension (elastic bands)•Torsion (twisted ropes)•Electrons ‘above’ protons

More general equation: PE = m * a * d

(See how………………. PE = m * g * h is the same, but more specific?)

5) A rollercoaster has a mass of 10,000 kg and gravity on earth has a strength of 10 m/s2. How much gravitational potential energy does the rollercoaster have if it is stopped at the highest point on the track, 75m above its lowest point?

1 2 3 4 5

89%

5%0%

5%0%

1. 7,500,000N2. 750,000N3. 1,000J4. 1333J5. None of the

above

Practice Problem

6) An elevator is connected to a counter-balancing mass. When the elevator goes up, the counterbalance goes down. The elevator by itself has a mass of 200 kg, and the people who get inside have a mass of 150 kg. The elevator goes up 30 m, while the counterbalance, which has a mass of 300 kg goes down 45 m. What is the total amount of energy input into the system?

Kinetic EnergyDefinition: The energy of a mass in motion.

Equation: KE = ½ m * v2

KE is Kinetic Energym is massv is velocity

The bigger it is, and the faster it is, the more ability to cause change it has.

Practice Problem7) A football player has a mass of 100 kg and is moving at 5 m/s. He accidentally runs into a goal post and comes to a complete stop. How much energy is transferred to the goal post?

Conservation of Energy

The total energy before equals the total energy after.

If it seems like some energy went missing, check for Thermal Energy (heat generation).

8) Wiley Coyote accidentally steps off of a 2000 m tall cliff. He has a mass of 10 kg. How fast will he be going when he hits the ground?

1 2 3 4 5

18%

12% 12%

6%

53%

1. 200,000J2. 20J3. 200 m/s4. 40,000 m/s5. None of the

above

9) A shopping cart starts at rest and rolls down a hill, picking up speed. At the bottom, it is going 4 m/s. How tall was the hill?

(You do not need to know the mass of the shopping cart to solve this. Set it up and see why.)

1 2 3 4 5

0%

25%

75%

0%0%

1. 0.4 m2. 0.8 m3. 40 m4. 80 m5. None of the

above

Power Practice Questions

1) A football player runs 50 m across the field exerting a downward force of 600 N and a sideways force of 25 N, over 5 seconds. A cheerleader jumps into the air, exerting a downward force of 600 N across a distance of 1 m in .2 seconds. How much power is exerted in each case?

2) A motorboat continually accelerates at 2 m/s2. It has a mass of 1000 kg. It does this for 5 seconds. If its power is 40,000 watts, then across what distance did it do this?

(You’ll need F = m * a, W = F * d, and P = W/t and lots of rearranging to solve this, OR you’ll need to use dimensional analysis to figure it out as you go.)

FlashcardsP = power Watts (W)W = work Joules (J)F = Force Newtons (N)p = momentum kg*m/s or N*s∆p = impulse kg*m/s or N*sm = mass kilograms (kg)a = acceleration meters/second2 (m/s2)v = velocity meters/second (m/s)d = distance meters (m)

P = W/tW = f*dF = m*ap = m*v∆p = F*tvf = vi +a*tdf = di +vi*t + ½ a t2