car with a mass of 1280 kg is moving around a curve with a radius of 50 m at a constant speed of 10 m/s (about 22 MPH).
(a) What is the centripetal acceleration of the car?
(b) What is the magnitude of the force required to produce this centripetal acceleration
To calculate the centripetal acceleration of the car and the magnitude of the force required to produce this acceleration, we can use the following formulas:
(a) Centripetal Acceleration (a) = v^2 / r
(b) Centripetal Force (F) = m * a
Given:
Mass of the car (m) = 1280 kg
Radius of the curve (r) = 50 m
Speed of the car (v) = 10 m/s
(a) Calculating the centripetal acceleration:
Using the formula, a = v^2 / r
Substituting the values, a = (10 m/s)^2 / 50 m
Simplifying, a = 100 m^2/s^2 / 50 m
a = 2 m/s^2
So, the centripetal acceleration of the car is 2 m/s^2.
(b) Calculating the magnitude of the centripetal force:
Using the formula, F = m * a
Substituting the values, F = 1280 kg * 2 m/s^2
Simplifying, F = 2560 N
So, the magnitude of the force required to produce this centripetal acceleration is 2560 Newtons.
a) v^2/R
b) m v^2/R