Question

The hero of a stunt film fires $50g$ bullets from a machine gun, each at a speed of $1.0km/s.$ If he fires 20 bullets in 4 seconds, what average force does he exert against the machine gun during this period.
A. $500N$
B. $250N$
C. $100N$
D. $300N$

Answer 1

In this case the rate of change of momentum is conserved. Momentum can be found by the product of the velocity and the mass of the respective object. So find the momentum for all the bullets fired, this is the total force impacted on the gun by the bullets. So this much force should be exerted against the gun by the person holding it.

Complete answer:
Given the mass of the bullet is = $50g$
The total number of bullets fired is = 20
Time taken to fire is = $4 seconds$
The velocity of the bullet fired is = $1.0km/s.$
So the momentum of the each bullet is = mass of the bullet $\times$ velocity of the bullet
Momentum of the each bullet = $0.050\times 1\times 1000\text{ kg}\cdot \text{m}\cdot {{\text{s}}^{-1}}\text{ =50kg}\cdot \text{m}\cdot {{\text{s}}^{-1}}\text{ }$
The total momentum of the bullets fired is = $\text{50}\times \text{20 kg}\cdot \text{m}\cdot {{\text{s}}^{-1}}\text{ = 1000kg}\cdot \text{m}\cdot {{\text{s}}^{-1}}$
The rate of change of momentum is = $\dfrac{1000\text{ kg}\cdot \text{m}\cdot {{\text{s}}^{-1}}}{4s}=250N$

Hence the option (B) is the correct answer.

Note:
In this case only momentum is conserved but energy is not conserved. The rate of change of momentum of the bullets fired is balanced by the person holding the gun by exerting the same force against the gun and hence the momentum is conserved. But the energy is not conserved, since the final energy of the bullet is with the combination of heat energy.