Question 1 (8 points)
You are going 30 m/s in a car of mass 1000 kg when you reach a red light and stop your car.
a. How much heat energy is released
... [Show More] by the brakes of your car?
b. If your car could recapture 40% of the heat energy released from your brakes, how much energy
would you recapture?
c. Imagine that you have an electric car and all of the recaptured energy is put back into the battery that
powers your car. What speed could your car achieve from rest by using only the recaptured energy from
part (b)?
d. If you brake from the speed in part (c) and then start again from rest, how fast will you be able to
drive?
e. An advertisement says that if you have regenerative brakes like these, you'll never have to put any
more energy into your car again. Is this true or false?
Question 2 (4 points)
Andrea rides her bicycle at a speed of 10 m/s. She and the bike have a combined mass of 50 kg.
a. If she uses her brakes to slow down to 5 m/s, how much energy is converted to heat?
Heat energy = ½ * 50 * 10^2 – ½ * 50 * 5^2 = 1875 J
b. Andrea has a particularly old bike, and she has not lubricated the chain or gears. This causes friction
inside the gears as she rides. She begins coasting on flat ground at a speed of 10 m/s, and after a few
seconds is only going 8 m/s. How much energy has been converted to heat?
c. Andrea is going 10 m/s toward a hill. She coasts up the hill without pedaling. If friction causes 10% of
her energy to be converted to heat inside the gears, how high up the hill will she be able to coast? (2
points)
Question 3 (7 points)
Josh sleds down a hill from a height of 35 m. He has a mass of 60 kg. He starts from rest at the top of the
hill.
a. If there were no friction, how fast would he be going when he reached the bottom of the hill?
b. In reality, the friction between the sled and the ground causes Josh to lose 15% of his initial energy as
heat. In this case, how fast will he be going when he reaches the bottom?
c. Josh is sledding into a valley that rises again on the other side. He can sled down one side and then
back up the other side. If he loses 15% of his initial energy to friction by the time he reaches the bottom,
then loses another 10% of his remaining energy sledding back up, how high can he slide up the other
side of the valley before he comes to a stop?
d. Instead of starting from rest, Josh starts with a speed of 10 m/s. How fast will he be going when he
reaches the bottom of the hill? (Assume no friction.)
Question 4 (6 points)
You release a pendulum of mass 1 kg from a height of 0.75 m.
a. If there is no air resistance, how fast is the pendulum going when it reaches the bottom?
b. If the pendulum loses 18% of its initial energy by the time it reaches the bottom, how fast is it going
when it reaches the bottom?
c. If the pendulum loses another 7% of its remaining energy by the time it reaches the other side, how
high up does it go?
d. After a few minutes, the pendulum is no longer swinging at all. Explain why this happens, in terms of
energy. [Show Less]