A roller coaster car of mass 312 kg (including passengers) travels around a horizontal curve of radius 35.7 m. Its speed is 16.4 m/s. What is the magnitude of the total force exerted on the car by the track?
Question
A roller coaster car of mass 312 kg (including passengers) travels around a horizontal curve of radius 35.7 m. Its speed is 16.4 m/s. What is the magnitude of the total force exerted on the car by the track?
Solution
To solve this problem, we need to use the formula for centripetal force, which is F = mv^2/r, where m is the mass, v is the velocity, and r is the radius of the curve.
Step 1: Identify the given values. The mass (m) of the roller coaster car including passengers is 312 kg. The speed (v) of the roller coaster car is 16.4 m/s. The radius (r) of the curve is 35.7 m.
Step 2: Substitute the given values into the formula. F = (312 kg) * (16.4 m/s)^2 / 35.7 m
Step 3: Calculate the force. F = 312 kg * 268.96 m^2/s^2 / 35.7 m F = 2352.3 N
So, the magnitude of the total force exerted on the car by the track is approximately 2352.3 Newtons.
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