Question

A car of mass \( 2000 kg \) rounds a curve of radius \( 250 m \) at \( 90 km / hr \). Calculate (a) its angular speed (b) its centripetal acceleration (c) the centripetal force acting on it.

Answer 1

Given

m = 2000 kg

R = 250 m

v = 90 × \(\frac{5}{18}\)

v = 25 m/s

(a) Angular speed ω = \(\frac{\text{v}}{R}\)

\(= \frac{25}{250}\)

\(= \frac{1}{10}\)

= 0.1 rad/sec

(b) Centripetal acceleration = \(\frac{\text{v}^2}{R}\)

\(=\frac{25 \times 25}{250}\)

= 2.5 m/s² 

(c) Centripetal force = \(\frac{M\text{v}^2}{R}\)

\(=\frac{2000 \times (25)^2}{250}\)

\(=\frac{2000 \times 25 \times 25}{250}\)

= 5000 N