What is the mass of the car?

Question

A rollercoaster track provides 6400 N of centripetal force on a rollercoaster car. The car travels at a speed of 22 m/s as it rounds a horizontal curve with a radius of 15 m. What is the mass of the car?

 

Show all work and explain using physics terms please.

Answer 1

Force is mass times acceleration.

 

 

F = ma

 

 

Centripetal force is mass times centripetal acceleration.

 

 

 F_c = ma_c

 

     = m(v²/r)

 

 

Solving for the mass of the car m, we get

 

 

m = F_c(r/v²)

 

 

The velocity of the car v is 22 m/s. 

 

The radius of the curve r is 15 m.

 

The centripetal force F_c  is 6,400 N

 

 

Plugging in the values, we get

 

 

m = (6,400N)[15m/(22m/s)²]

 

    = 198 kg

 

 

So the mass of the car m  is 198 kg.

 

 

We can double check this mass by plugging it into the centripetal force equation. If the statement is true, then the mass m  is correct.

 

 

F_c = m(v²/r)

 

6,400 N  = (198kg)[(22m/s)²/(15m)]

 

6,400 N ≈ 6,389 N

 

 

The statement is more or less true, so the mass m = 198 kg is correct.

 

I hope this helped.

 

     

 

Answer 2

Fc = mv^2 / r

 

Given:  Fc = 6400 N

 

m = (r / v^2 ) * Fc = [15 m / (22 m/s)^2] * 6400 N = 198.3 kg