The 43.0 kg man in the roller coaster car is sitting on a bathroom scale. If he is traveling at 39.7 m/s exactly halfway up the loop and the radius of the vertical coaster track is 66.9 meters, what does the scale read (in newtons)?

The scale reads a force of 21243.83 N, which is the combination of centripetal and gravitational forces acting on the man in the roller coaster halfway up the vertical coaster track.

Explanation:

This query involves the application of physics principles related to centripetal force.

The force acting on the man when he's halfway up the vertical coaster track is a combination of gravitational force and centripetal force. To determine what the scale reads, we need to consider both forces using the following formulas:

Centripetal Force (Fc) = mass (m) x velocity2 (v2) / radius (r)
Gravitational Force (Fg) = mass (m) x gravity (g)

First, we calculate centripetal and gravitational forces:

Fc = 43.000 kg x (39.700 m/s)2 / 66.900 m = 20,822 N
Fg = 43.000 kg x 9.81 m/s2 = 421.83 N

Since he is halfway up, the centripetal force and gravitational force act towards the center of the loop. Therefore, the scale reading will be the sum of these two forces (Fc + Fg) = 20,822 N + 421.83 N = 21243.83 N, which is what the scale reads.

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