Question

Bullets of 40 g mass each hit a plate at the rate of 100
bullets per second, with a velocity of 60 m/s and
reflect back with a velocity of 30 m/s. The average
force acting on the plate is​

Answer 1

Answer:

360 N

Explanation:

Given :

Bullets of 40 g mass each hit a plate at the rate of 100  bullets per second, with a velocity of 60 m/s and  reflect back with a velocity of 30 m/s.

To find :

the average  force acting on the plate

Solution :

The bullets hit the plate at the rate of 100 bullets per second.

In one second, 100 bullets hit the plate.

Mass of each bullet, m = 40 g

Mass of 100 bullets, M = 100 × 40 g = 4000 g = 4 kg

They hit with the velocity 60 m/s and reflect back with 30 m/s.

So, initial velocity, u = 60 m/s

final velocity, v = 30 m/s

The average force acting on the plate is rate of change in momentum.

 $\longrightarrow \sf F=\dfrac{dP}{dt}$

Change in momentum = Mv - Mu

dP/dt  = M(v - u)

dP/dt  = 4(30 - (-60))  [ u is taken -ve as the bullets reflect back ]

dP/dt  = 4(30 + 60)

dP/dt  = 4(90)

dP/dt  = 360 kg m/s

The average force acting on the plane = dP/dt

  = 360/1

  = 360 N