Hi folks,
Today we took the time to really work with the three major energy formulas and tackle several problems.
For homework this week answer the following problems. I've included answers to the math problems below. These will be quizzed on next week so please take the time to really get to know these.
1. Assume the following to answer the questions below:
Mass of ball = .05 kg
Height of ramp = .032 m
Ave. velocity of ball on ramp = .4 m/s
Distance ball rolled after getting off ramp = 3 m
a. What makes the ball stop after getting off the ramp?
b. What was the velocity of the ball at the very bottom of the ramp? (Careful here!)
c. What was the gPE of the ball at the top of the ramp?
d. What was the gPE of the ball at the bottom of the ramp?
e. What happened to the gPE?
f. What was the KE of the ball at the bottom of the ramp?
g. Where did the energy of the system originally come from?
h. What amount of work did friction do to the ball after it got off the ramp to the point where the ball stopped rolling?
i. Where did the energy go that caused the ball to stop?
j. What is the friction force of the carpet on the ball?
2. Thinking about the energy formulas, tell me if it make sense to have a heavy vehicle or a light vehicle as far as gPE goes.
3. If you created a balloon powered car, would you want it to be heavy? Why or why not?
4. If you and a friend were on identical sleds and your friend weighs twice as much as you do, which of you would go farther? Which of you would have more velocity? Describe this in relation to momentum and describe this in relation to energy.
Use these formulas to solve the following Olympic energy problems. Answers below.
gPE = MgH
KE = ½ MV^2 (^2 means squared)
W = FD
5. A ski jumper who has a mass of 80 kg stands at the top of a ski jump that is 15m tall.
a. What is his potential energy?
b. If there's no friction, what would his speed be as he launches from the jump?
c. If his speed is 13 m/s, what is the energy efficiency of the ramp?
d. What work did friction do on our ski hero?
e. What was the average force of friction between the ramp and his skis if he travels
75 m down the ramp
6. a. If the Irish bob sled with a mass of 320 kg reaches a top speed of 48 m/s, what was the least amount of energy the bob sled started with?
b. What was the lowest height the bob sled started at?
c. If the stopping area of the track is 30m long, what work will friction do on our Irish bob sledders by the time the team comes to a complete rest at the bottom?
d. If the height of the track was really 200 m, what was the energy efficiency of the bob sled?
Answers to math problems
1. b. .8 m/s (twice the average speed)
c. gPE = .05 x 10 x .032
gPE = .016 J
d. 0 J
f. KE = 1/2 .05kg x (.8m/s)^2
KE = .016 J
h. Work due to friction = .016J
j. .016 = F x 3
. 0053 N = F
5. a. gPE = Mgh
80 kg x 15 m x 10 m/s^2 = 12,000J
b. KE = ½ MV^2
12,000 J = ½ 80 kg x v^2
v = 17.3 m/s
c. KE = ½ 80kg x (13m/s)^2
KE = 6760 J
Work out/ Work in x 100
6760/12000 x 100 = 56% Efficient
d. 12,000J - 6760J = 5240 J amount of energy friction stole
e. W = FD
5240J = F x 75m
F = 69.9 N amount of force friction applied to skier
6. a. KE = ½ MV^2
KE = ½ 320kg (48 m/s)^2
KE = 368,640 J
b. gPE = MgH
368,640 = 320kg x 10m/s^2 x H
H = 115.2 m (That's some ramp!)
c. W = FD
368,640 J = F x 30 m
F = 12,288 N (A typical car braking force is 15,000N)
d. gPE = MgH
gPE = 320 kg x 10 m/s^2 x 200 m
gPE = 640,000 J That's the maximum amount of energy. Since their energy was 368,640 J their energy efficiency was…
Work out / Work in x 100
368,640/ 640,000 x 100 = 58%
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