ROLLER COASTER QUESTIONS Understanding Conservation of Energy and

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 30 m E F 18 m D B

ROLLER COASTER QUESTION 1 • At what location between A and E is the cart moving the fastest? A C 30 m E F 18 m D B

ANSWER QUESTION 1 • B

ROLLER COASTER QUESTION 2 • At what location between A and E is the cart moving the slowest? A C E 30 m F 18 m D B

ANSWER QUESTION 2 • A

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

ANSWER QUESTION 3 • B>D>E>C>A

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

ANSWER QUESTION 4 • CHOICE A: BETWEEN A AND B

ROLLER COASTER QUESTION 5 • What force is causing the cart to stop between E and F? A C E 30 m F 18 m D B

ANSWER QUESTION 5 • The Force of Friction

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 30 m F 18 m D B

ANSWER QUESTION 6 Friction Force Normal Force Gravitational Force

ROLLER COASTER QUESTION 7 • What is the net Force between E and F? A C E 30 m F 18 m D B

ANSWER QUESTION 7 • Net Force = Friction Force

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 30 m F 18 m D B

ANSWER QUESTION 9 • THIS IS A “TRICK” QUESTION. ALL THE MECHANICAL ENERGIES ARE THE SAME AT ALL LOCATIONS.

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 30 m F 18 m D B

ANSWER QUESTION 10 PE i + Kei = PEf + KEf mghi + 1/2 mvi 2 = mghf + 1/2 mvf 2 ghi + 1/2 vi 2 = ghf + 1/2 vf 2 (9. 8 m/s 2)(30 294 m/s)2 m) + 1/2(20 = 0 + 1/2 vf 2 m 2/s 2 + 200 m 2/s 2 = 1/2 vf 2 494 m 2/s 2 = 1/2 vf 2 988 m 2/s 2 = vf 2 31. 4 m/s = v f A C 30 m B E D F 18 m

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 30 m F 18 m D B

ROLLER COASTER QUESTION 11 • c. More than 20 m/s

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 30 m F 18 m D B

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 30 m F 18 m D B

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 30 m ? B F 18 m D

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 mvi 2 = mghf + 1/2 mvf 2 ghi + 1/2 vi 2 = ghf + 1/2 vf 2 (9. 8 m/s 2)(30 m) + 1/2(20 m/s)2 = (9. 8 m/s 2)(h) + 1/2(1 m/s)2 294 m 2/s 2 + 200 m 2/s 2 = 9. 8 m/s 2 (h) + ½(1 m/s)2 494 m 2/s 2 = 9. 8 m/s 2 (h) + 0. 5 m 2/s 2 493. 5 m 2/s 2 = 9. 8 m/s 2 (h) 50. 3 m = h

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. Athe cart at E? C E 30 m F 18 m D B

ROLLER COASTER QUESTION 14 PEi + KEi = PEf + KEf mghi + 1/2 mvi 2 = mghf + 1/2 mvf 2 ghi + 1/2 vi 2 = ghf + 1/2 vf 2 (9. 8 m/s 2)(30 m) + 1/2(20 m/s)2 = (9. 8 m/s 2)(18 m) + 1/2 vf 2 294 m 2/s 2 + 200 m 2/s 2 = 176. 4 m 2/s 2 317. 6 m 2/s 2 = 1/2 vf 2 635. 2 m 2/s 2 = vf 2 25. 2 m/s = v f + 1/2 vf 2 A C 3 0 m B E D F 18 m

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

ROLLER COASTER QUESTION 15 • 113 m Fd = 1/2 mvf 2 - 1/2 mvi 2 µmgd = 1/2 mvf 2 - 1/2 mvi 2 µgd = 1/2 v f 2 - 1/2 vi 2 µgd = 0 - 1/2 vi 2 d = 1 v i 2/µg d = (35 m/s) 2/(. 55)(9. 8 d = 113 m A C E 30 m B m/s 2 D F 18 m