1. ROLLER COASTER QUESTIONS
Understanding Conservation of Energy and Work-Energy Theorem

2. Roller Coaster
The roller coaster is frictionless from Location A to E and has friction for braking between E and F.
30 m
18 m A B C D E F

3. Roller Coaster QUESTION 1
At what location between A and E is the cart moving the fastest?
30 m
18 m A B C D E F

4. Answer Question 1 B

5. Roller Coaster QUESTION 2
At what location between A and E is the cart moving the slowest?
30 m
18 m A B C D E F

6. Answer Question 2 A

7. Roller Coaster QUESTION 3
List the five locations A to E in order of the amount of KE the cart possesses at that location. List from Largest to Smallest.
30 m
18 m A B C D E F

8. B>D>E>C>A
Answer Question 3
B>D>E>C>A

9. Roller Coaster QUESTION 4
Between what two locations if the change in KE the largest? (consider the absolute value for the change)
Between A and B
Between B and C
Between C and D
Between D and E
Between B and D
Between A and E
30 m
18 m A B C D E F

10. Answer Question 4
CHOICE A: BETWEEN A AND B

11. Roller Coaster QUESTION 5
What force is causing the cart to stop between E and F?
30 m
18 m A B C D E F

12. Answer Question 5
The Force of Friction

13. Roller Coaster QUESTION 6
Friction causes the cart to stop only between E and F. Draw a force diagram for the cart between E and F.
30 m
18 m A B C D E F

14. Answer Question 6
Friction Force
Normal Force
Gravitational Force

15. Roller Coaster QUESTION 7
What is the net Force between E and F?
30 m
18 m A B C D E F

16. ANSWER QUESTION 7
Net Force = Friction Force

17. Roller Coaster QUESTION 9
Compare the Mechanical Energy of the Cart at Location A thru E.
List the Mechanical energies from Largest to Smallest.
30 m
18 m A B C D E F

18. Answer Question 9
THIS IS A “TRICK” QUESTION. ALL THE MECHANICAL ENERGIES ARE THE SAME AT ALL LOCATIONS.

19. Roller Coaster QUESTION 10
At position A the roller coaster cart is traveling at 20. m/s. If the vertical distance between position A and B is 30. m, what is the speed of the cart at B?
30 m
18 m A B C D E F

20. Answer Question 10 A C E F D B PEi + Kei = PEf + KEf
mghi + 1/2 mvi2 = mghf + 1/2 mvf2
ghi + 1/2 vi2 = ghf + 1/2 vf2
(9.8 m/s2)(30 m) + 1/2(20 m/s)2 = 0 + 1/2vf2
294 m2/s m2/s2 = 1/2vf2
494 m2/s2 = 1/2vf2
988 m2/s2 = vf2
31.4 m/s = vf
30 m
18 m A B C D E F

21. Roller Coaster QUESTION 11
If the Roller Coaster Cart is moving at 20 m/s at position A, then what speed would be possible at Position D? a. Less than 20 m/s b. 20 m/s c. More than 20 m/s
30 m
18 m A B C D E F

22. Roller Coaster QUESTION 11
c. More than 20 m/s

23. Roller Coaster QUESTION 12
If the Roller Coaster Cart is moving at 20 m/s at position A, can C have a height higher than hill A?
30 m
18 m A B C D E F

24. Roller Coaster Question 12
Yes. As long as the TME (KE + PE) at hill C is not larger than the TME (KE + PE) at hill A.
30 m
18 m A B C D E F

25. Roller COASTER QUESTION 13
How high can Hill C be to have a cart roll over it at a speed of 1 m/s. Assuming the cart travels over Hill A at 20 m/s?
30 m
18 m A B C D E F ?

26. Roller COASTER QUESTION 13
How high can Hill C be to have a cart roll over it at a speed of 1 m/s. Assuming the cart travels over Hill A at 20 m/s?
PEi + KEi = PEf + KEf
mghi + 1/2 mvi2 = mghf + 1/2 mvf2
ghi + 1/2 vi2 = ghf + 1/2 vf2
(9.8 m/s2)(30 m) + 1/2(20 m/s)2 = (9.8 m/s2)(h) + 1/2(1 m/s)2
294 m2/s m2/s2 = 9.8 m/s2 (h) + ½(1 m/s)2
494 m2/s2 = 9.8 m/s2 (h) m2/s m2/s2 = 9.8 m/s2 (h) m = h

27. Roller Coaster QUESTION 14
If the vertical distance from B to E is 18 m and the speed of the cart at A is 20 m/s, then what is the velocity of the cart at E?
30 m
18 m A B C D E F

28. Roller Coaster QUESTION 14
PEi + KEi = PEf + KEf mghi + 1/2 mvi2 = mghf + 1/2 mvf2 ghi + 1/2 vi2 = ghf + 1/2 vf2 (9.8 m/s2)(30 m) + 1/2(20 m/s)2 = (9.8 m/s2)(18 m) + 1/2vf2 294 m2/s m2/s2 = m2/s2 + 1/2vf m2/s2 = 1/2vf m2/s2 = vf m/s = vf
30 m
18 m A B C D E F

29. Roller Coaster QUESTION 15
If the velocity at E is 35 m/s and the coefficient of friction between E and F is 0.55, than what distance will the cart travel before coming to a stop?
30 m
18 m A B C D E F

30. Roller Coaster QUESTION 15
113 m
Fd = 1/2mvf2 - 1/2mvi2
µmgd = 1/2mvf2 - 1/2mvi2
µgd = 1/2vf2 - 1/2vi2
µgd = /2vi2
d = 1vi2/µg
d = (35 m/s) 2/(.55)(9.8 m/s2
d = 113 m
30 m
18 m A B C D E F