A roller-coaster car has a mass of 500 kg when fully loaded with passengers.The car passes over a hill of radius 15 m,as shown.At the top of the hill,the car has a speed of 8.0 m/s.What is the force of the track on the car at the top of the hill?
A)7.0 kN up
B)7.0 kN down
C)2.8 kN down
D)2.8 kN up
E)5.6 kN down

Question

A roller-coaster car has a mass of 500 kg when fully loaded with passengers.The car passes over a hill of radius 15 m,as shown.At the top of the hill,the car has a speed of 8.0 m/s.What is the force of the track on the car at the top of the hill? 
A)7.0 kN up 
B)7.0 kN down 
C)2.8 kN down 
D)2.8 kN up 
E)5.6 kN down

Quizplus · Accepted Answer

At the top of the hill, the car is at the highest point of the roller-coaster, so there is only a normal force and gravitational force acting on the car:

$F_	ext{net} = F_	ext{N} - F_	ext{g} = m a$

where $m$ is the mass of the car and $a$ is the acceleration of the car. Since the car is moving at a constant speed of 8.0 m/s, we know that $a = 0$, so:

$F_	ext{N} - F_	ext{g} = 0$

$F_	ext{N} = F_	ext{g}$

$F_	ext{N} = m g$

where $g$ is the acceleration due to gravity ($9.81 m/s^2$).

At the top of the hill, the normal force is pointing upwards (perpendicular to the track), so the force of the track on the car is equal in magnitude but opposite in direction to the normal force:

$F_	ext{track} = - F_	ext{N}$

$F_	ext{track} = - m g$

$F_	ext{track} = -(500	ext{ kg})(9.81	ext{ m/s}^2)$

$F_	ext{track} = -4905	ext{ N}$

$F_	ext{track} = 2.8	ext{ kN up}$

So the force of the track on the car at the top of the hill is 2.8 kN, which is upward. The correct answer is D.

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