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. 30 m 18 m A B C D E F

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

Answer Question 1 B

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

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. List from Largest to Smallest. 30 m 18 m A B C D E F

B>D>E>C>A 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) 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

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? 30 m 18 m A B C D E F

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. 30 m 18 m A B C D E F

Answer Question 6 Friction Force Normal Force Gravitational Force

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

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. 30 m 18 m A B C D E F

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? 30 m 18 m A B C D E F

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/s2 + 200 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

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

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? 30 m 18 m A B C D E F

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

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 ?

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/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

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

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/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 30 m 18 m A B C D E F

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

Roller Coaster QUESTION 15 113 m Fd = 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 30 m 18 m A B C D E F