Energy Transfer….

Examples of lots of Kinetic Energy

What about this one….

So what does K depend on?

• Kinetic Energy depends not only on the speed, but also the mass of the object.

• K = ½ mv2

• Increasing velocity has a greater effect than increasing mass

Proportional Reasoning

• What would happen to the kinetic energy of an object if I….

• Doubled the mass?• Quadrupled the mass?• Cut the mass by 1/3?

Proportional Reasoning

• What would happen to the kinetic energy of an object if I….

• Doubled the velocity? • Quadrupled the velocity?• Cut the velocity by 1/3?

4x

Calculations

• Usain Bolt has a mass of 94 kg and can reach a speed of 12.2 m/s. Calculate his K.

• At 31 m/s, the cheetah has 28,830 J of kinetic energy. Calculate his mass.

• T-Rex has a mass of 6,000 kg and has 192,000 J of kinetic energy. Calculate his velocity.

Show car video

video_car_sliding_across.mov

Show sliding car

Now it’s time for calculations…Here is a graph of v vs. t….What is the car’s initial velocity?What is the car’s final velocity?Mass of the prius is roughly 2,000 kgCalculate the change in kinetic energy…

• Draw Free Body Diagram for the car after applying the brakes…• What direction is the car moving?• What direction is friction?• What does this tell you about the work being

done on the car?

Calculating Work

• W = F x d• Force – Only force doing work is friction, and

Newton’s 2nd Law states that F = ma.• W = (ma) x d• We know the mass of the prius, but what

about its acceleration?

Looking back….

• How did we find acceleration from a v vs. t graph?

Calculating Work…

• We had the equation, W = (ma) x d• We now know m and a…• What about the distance travelled?• How can we get it from the v vs. t graph?• Area….but that isn’t a pretty shape.

x vs. t graph is WAY easier

Calculating Work…

• We’re still doing this?!?

Calculating Work…

• W = (ma) x d• W = 2000 kg x 1.9515 m/s/s x -8.38 m• W = -32,707.14 J

But wait…• We said the change in kinetic energy was -

32,670 J• And the work done by friction was equal to

-32,707 J.• That’s because….

W = ΔKWork-Energy

Theorem

• That’s because….W = ΔK

Work-Energy Theorem