Question

A car with a mass of 1,200 kilograms is moving around a circular curve at a uniform velocity of 20 meters per second. The centripetal force on the car is 6,000 newtons. what is the radius of the curve?

Answer 1

The answer is 80 m.

Centripetal force (F) is a force that makes body move around a circular curve. The unit of force is N (N = kg * m/s²).
It can be represented as:

`F= (m* v^(2) )/(r)`
where:
m - mass
v - velocity
r - radius of the curve

We have:
m = 1,200 kg
V = 20 m/s
F = 6,000 N = 6,000 kg * m/s²

We need radius of the curve:
r = ?

So, if
`F= (m* v^(2) )/(r)`, then:

`r= (3* v^(2) )/(F)`
⇒
`r = (1200 kg * (20m/s)^(2) )/(6000 kg*m/s^(2) )`
⇒
`r= (1200*400*kg*m^(2)*s^(2) )/(6000kg*m/s^(2) )`
⇒
`r= (480,000m)/(6000)`
⇒
`r=80m`