A roller-coaster car has a mass of 500 kg when fully loaded with passengers.At the bottom of a circular dip of radius 40 m (as shown in the figure)the car has a speed of 16 m/s.What is the magnitude of the force of the track on the car at the bottom of the dip?
A)3.2 kN
B)8.1 kN
C)4.9 kN
D)1.7 kN
E)5.3 kN

Question

A roller-coaster car has a mass of 500 kg when fully loaded with passengers.At the bottom of a circular dip of radius 40 m (as shown in the figure)the car has a speed of 16 m/s.What is the magnitude of the force of the track on the car at the bottom of the dip? 
A)3.2 kN 
B)8.1 kN 
C)4.9 kN 
D)1.7 kN 
E)5.3 kN

Quizplus · Accepted Answer

The force of the track on the car is the sum of the gravitational force (weight) and the centripetal force.

The weight can be calculated as:
W = m*g = 500 kg * 9.8 m/s^2 = 4900 N

The centripetal force can be calculated as:
F_c = m*v^2/r = 500 kg * (16 m/s)^2 / 40 m = 3200 N

Therefore, the magnitude of the force of the track on the car at the bottom of the dip is:
F = W + F_c = 4900 N + 3200 N = 8100 N = 8.1 kN.

So, the best choice is B.

A Roller-Coaster Car Has a Mass of 500 Kg When