A car with a mass of 1380 kg is moving around a curve with a radius of 50 m at a constant speed of 25 m/s (about 56 MPH).
(a) What is the centripetal acceleration of the car?
1 m/s2
(b) What is the magnitude of the force required to produce this centripetal acceleration?
2 N
To find the centripetal acceleration of the car, we can use the formula:
a = v^2 / r
where:
a = centripetal acceleration
v = velocity of the car
r = radius of the curve
In this case, the velocity (v) of the car is given as 25 m/s, and the radius (r) of the curve is 50 m. Plugging these values into the formula, we have:
a = (25 m/s)^2 / 50 m
a = 625 m^2/s^2 / 50 m
a = 12.5 m/s^2
Therefore, the centripetal acceleration of the car is 12.5 m/s^2.
To find the magnitude of the force required to produce this centripetal acceleration, we can use the formula:
F = m * a
where:
F = force required
m = mass of the car
a = centripetal acceleration
The mass (m) of the car is given as 1380 kg, and the centripetal acceleration (a) is calculated as 12.5 m/s^2. Plugging these values into the formula, we have:
F = 1380 kg * 12.5 m/s^2
F = 17,250 kg·m/s^2
Since the unit for force is newtons (N), we need to convert the unit for kilogram meter per second squared (kg·m/s^2) to newtons. 1 newton is equal to 1 kilogram meter per second squared, so we can simply say:
F = 17,250 N
Therefore, the magnitude of the force required to produce this centripetal acceleration is 17,250 N.