FIGURE 8-6 A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in Figure 8-6. The vertical height at position A above ground level is 200 m. Neglect friction and use g = 10.0 m/s 2 .
-What is the total energy of the roller coaster at point B?

Question

FIGURE 8-6  A roller coaster of mass 80.0 kg is moving with a speed of 20.0 m/s at position A as shown in Figure 8-6. The vertical height at position A above ground level is 200 m. Neglect friction and use g = 10.0 m/s 2 .
-What is the total energy of the roller coaster at point B?

Quizplus · Accepted Answer

At point A, the roller coaster has both kinetic energy and gravitational potential energy, given by 
KE = (1/2)mv^2 = (1/2)(80.0 kg)(20.0 m/s)^2 = 16,000 J 
PE = mgh = (80.0 kg)(10.0 m/s^2)(200 m) = 160,000 J

At point B, the roller coaster has lost gravitational potential energy but gained kinetic energy. Since there is no friction, mechanical energy is conserved so the total energy at point B is equal to the total energy at point A. Therefore, 
Total energy at point B = KE + PE = 16,000 J + 160,000 J = 176,000 J

The closest answer choice is C, 17.6 × 10^3 J.

FIGURE 8-6 a Roller Coaster of Mass 80