14. 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?
To find the radius of the curve, we can use the formula for centripetal force:
F = (mv^2) / r
Where:
F = centripetal force
m = mass of the car
v = velocity of the car
r = radius of the curve
In this case, we are given:
F = 6,000 N
m = 1,200 kg
v = 20 m/s
We can rearrange the formula to solve for r:
r = (mv^2) / F
Plugging in the values, we can calculate the radius:
r = (1,200 kg * (20 m/s)^2) / 6,000 N
r = (1,200 kg * 400 m^2/s^2) / 6,000 N
r = 480,000 kg * m^2/s^2 / 6,000 N
r = 80 m
Therefore, the radius of the curve is 80 meters.