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ROLLER COASTER QUESTIONS

ROLLER COASTER QUESTIONS. Understanding Conservation of Energy and Work-Energy Theorem. Roller Coaster. The roller coaster is frictionless from Location A to E and has friction for braking between E and F. A. C. E. F. 30 m. 18 m. D. B. Roller Coaster QUESTION 1.

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ROLLER COASTER QUESTIONS

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  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. A C E F 30 m 18 m D B

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

  4. Answer Question 1 • B

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

  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. A C E F 30 m 18 m D B

  8. 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 A C E F 30 m 18 m D B

  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? A C E F 30 m 18 m D B

  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. A C E F 30 m 18 m D B

  14. Answer Question 6 Friction Force Normal Force Gravitational Force

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

  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. A C E F 30 m 18 m D B

  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? A C E F 30 m 18 m D B

  20. Answer Question 10 PEi + Kei = PEf + KEf mghi + 1/2 mvi2 = mghf + 1/2 mvf2 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/s2 + 200 m2/s2 = 1/2vf2 494 m2/s2 = 1/2vf2 988 m2/s2 = vf2 31.4 m/s = vf A C E F 30 m 18 m D B

  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 A C E F 30 m 18 m D B

  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? A C E F 30 m 18 m D B

  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. A C E F 30 m 18 m D B

  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? ? A C E F 30 m 18 m D B

  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 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/s2 + 200 m2/s2 = 9.8 m/s2 (h) + ½(1 m/s)2 494 m2/s2 = 9.8 m/s2 (h)+ 0.5 m2/s2 493.5 m2/s2 = 9.8 m/s2 (h) 50.3 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? A C E F 30 m 18 m D B

  28. Roller Coaster QUESTION 14 PEi + KEi = PEf + KEf mghi + 1/2 mvi2 = mghf + 1/2 mvf2 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/s2 + 200 m2/s2 = 176.4 m2/s2 + 1/2vf2 317.6 m2/s2 = 1/2vf2 635.2 m2/s2 = vf2 25.2 m/s = vf A C E F 30 m 18 m D B

  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? A C E F 30 m 18 m D B

  30. Roller Coaster QUESTION 15 • 113 m Fd = 1/2mvf2 - 1/2mvi2 µmgd = 1/2mvf2 - 1/2mvi2 µmgd = 1/2mvf2 - 1/2mvi2 µgd = 1/2vf2 - 1/2vi2 µgd = 0- 1/2vi2 d = 1vi2/µg d = (35 m/s) 2/(.55)(9.8 m/s2 d = 113 m A C E F 30 m 18 m D B

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