Question

The velocity of a body of mass 10 kg increases from 4 m/s to 8 m/s when a force acts on it for 2 s.
(a) What is the momentum before the force acts?
(b) What is the momentum after the force acts?
(c) What is the gain in momentum per second?
​(d) What is the value of the force?

Answer 1

(a) Mass of the body = 10 kg

Velocity before the force acts = 4 m/s

Momentum before the force acts = Mass $\times$ Velocity = 10 kg $\times$ 4 m/s = 40 kg m/s

(b) Mass of the body = 10 kg

Velocity after the force acts = 8 m/s

Momentum after the force acts = Mass $\times$ Velocity = 10 kg $\times$ 8 m/s = 80 kg m/s

(c) Gain in momentum = Final momentum $-$ Initial momentum = 80 kg m/s $-$ 40 kg m/s = 40 kg m/s

Time taken = 2 s

The gain in momentum per second = $\frac{40\mathrm{kg}\mathrm{m}/\mathrm{s}}{2\mathrm{s}}=20\mathrm{kg}\mathrm{m}/{\mathrm{s}}^2$

(d) Force is defined as the rate of change of momentum. Hence, force is equal to the change in momentum per second i.e. 20 N