A car of mass m = 1000 kg moves in a horizontal circle of radius r = 50 m at a speed of v = 10 m/s. Find the centripetal acceleration of the car and the force acting on it.
m = 1000 kg
r = 50 m
v = 10 m/s
For uniform circular motion $$a = \frac{v^2}{r}$$
The acceleration is already known — now apply Newton's second law: F = ma.
1. Centripetal acceleration:
$$a = \frac{v^2}{r} = \frac{10^2}{50} = \frac{100}{50} = 2 \text{ m/s}^2$$2. By Newton's second law:
$$F = ma = 1000 \cdot 2 = 2000 \text{ N}$$This force (the friction of the tyres on the road) is directed toward the centre of the circle.
a = 2 m/s², F = 2000 N (2 kN)