Robert D. answered 06/01/16
College Physics Grad with Extensive Tutoring Experience
Force is mass times acceleration.
F = ma
Centripetal force is mass times centripetal acceleration.
Fc = mac
Solving for the mass of the car m, we get
m = Fc(r/v2)
The velocity of the car v is 22 m/s.
The radius of the curve r is 15 m.
The centripetal force Fc 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.
Fc = 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.