Question

A car of mass 2000 kg moves round a curve of radius 250 m at 90 km/hr. Compute its

i. angular speed

ii. centripetal acceleration

iii. centripetal force.

Answer 1

Given: m = 2000 kg, r = 250 m

v = 90 km/v  = 90 x 5/18 = 25 m/s

To find:

i. Angular speed (ω)

ii. Centripetal acceleration (a_CP)

iii. Centripetal force (F_CP)

Formulae: i. ω = v/r ii. a_CP = ω²r

iii. F_CP = mv²/r

Calculation: i. From formula (i),

ω = \(\cfrac{25}{250}\)

\(\therefore\) ω = 0.1 rad/s

ii. From formula (ii),

a_CP = (0.1)² x 250

\(\therefore\) a_CP = 2.5 m/s²

iii. From formula (iii),

The car has,

i. angular speed 0.1 rad/s.

ii. centripetal acceleration 2.5 m/s² .

iii. centripetal force 5000 N.