A roller coaster car is loaded with passengers and has a mass of 500 kg along with a speed of 18 meters/second at the dip. The radius of curvature of the track at the bottom point of the dip is 12 meters (gravity = 9.8 meters/second2). What force is exerted on the roller coaster car by the track at the bottom of the dip?
A.
1.6 × 104 newtons
B.
1.8 × 104 newtons
C.
0.5 × 104 newtons
D.
1.0 × 104 newtons
E.
8.6 × 103 newtons

Question

A roller coaster car is loaded with passengers and has a mass of 500 kg along with a speed of 18 meters/second at the dip. The radius of curvature of the track at the bottom point of the dip is 12 meters (gravity = 9.8 meters/second2). What force is exerted on the roller coaster car by the track at the bottom of the dip?
A. 
1.6 × 104 newtons
B. 
1.8 × 104 newtons
C. 
0.5 × 104 newtons
D. 
1.0 × 104 newtons
E. 
8.6 × 103 newtons

Vocaloid · Answer

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sorry if this diagram is a little messy but I'll try to explain

the car goes through a "dip" that is roughly a circle with radius of curvature = 12 m

the car experiences a centripetal force towards the center of the circle, as well as a normal force upwards

to find the centripetal force:

Fc = mv^2 / r (plug in the radius, mass, and velocity and calculate Fc)

to find the normal force: in order for the car to stay on the track, the normal force Fn = gravity Fg

so Fn = Fg = mg, plug in mass and the gravitational constant and evaluate

finally, for the combined force, add Fc + Fn