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

To find the force of the track on the car, we need to use the centripetal force formula:
$$F_{c} = \frac{mv^{2}}{r}$$

where $m$ is the mass of the car, $v$ is the speed of the car, and $r$ is the radius of the circular dip.

Substituting the given values, we get:
$$F_{c} = \frac{(500 kg)(16 m/s)^{2}}{40 m} = 3.2 	imes 10^{3} N = 3.2 kN$$

Therefore, the magnitude of the force of the track on the car at the bottom of the dip is 3.2 kN, which is choice B.

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