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?
A. 80 meters
B. 32 meters
C. 16 meters
D. 160 meters
Solve this for R:
mass x acceleration = M*V^2/R = 6000 n
The answer is actaully a. Radius equals mass times velocity squared divided by force. Which in this case would be 1,200 x 20(2) / 6,000 which equals 80
To find the radius of the curve, we can use the centripetal force formula:
F = (m * v^2) / r
Where:
F is the centripetal force (6,000 N)
m is the mass of the car (1,200 kg)
v is the velocity of the car (20 m/s)
r is the radius of the curve (unknown)
Rearranging the formula, we get:
r = (m * v^2) / F
Plugging in the values, we get:
r = (1,200 kg * (20 m/s)^2) / 6,000 N
Simplifying the equation, we have:
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.
The correct answer is option A.