Question

a machine gun mounted on a 2000kg car,on a horizontal frictionless surface fires 10 bullets per second.if the mass of each bullet is 10 gram and velocityof each bulletis 500 m/s, then find the acceleration of car will be

Answer 1

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Answer 2

The acceleration of car will be $\bold{=0.025\ \mathrm{m} / \mathrm{s}^{2}}$.

The machine gun mounted over car having frictionless surface has the firing occurred of 10 bullets per second. This acceleration required is calculated through momentum.

Given:

Mass of car $\mathrm{m}_{\mathrm{car}} = 2000\ kg$

Mass of bullet $\mathrm{m}_{\text { bullet }}=10 \mathrm{g}=0.001\ \mathrm{kg}$

Velocity of bullet = 500 m/s

Momentum attained by every bullet $=\text { mass of bullet } \times \text { velocity of bullet }$

$\mathrm{P}_{\text { bullet }}=\mathrm{m}_{\text { bullet }}\times \mathrm{v}_{\text { bullet }}$

$\mathrm{P}_{\text { bullet }}=0.001\ \mathrm{kg} \times 500\ \mathrm{m} / \mathrm{s}$

$\mathrm{P}_{\text { bullet }}=5\ \mathrm{kg} \mathrm{m} / \mathrm{s}$

Total force exerted by the bullet over car is the sum of all momentum of bullets fired per second.

Force on car $= \text {number of bullet per second} \times \mathrm{P}_{\text { bullet }}$

Force $=10 \text { bullet per sec } \times 5\ \mathrm{kg} \mathrm{m} / \mathrm{s}$

Force $=10\ s^{-1} \times 5\ \mathrm{kg} \mathrm{m} / \mathrm{s}$

Force $=50\ \mathrm{kg} \mathrm{m} / \mathrm{s}^{2}$

Force = 50 N

Force on car $=\text { mass of car } \times \text {acceleration of car}$

Force $=\mathrm{m}_ \text { car } \times \mathrm{acceleration}_ \text { car }$

$50=2000 \times \mathrm{acceleration}_\text { car }$

$\bold{\mathrm{Acceleration}_ \text { car }=0.025\ \mathrm{m} / \mathrm{s}^{2}}$