Question

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

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Answer 1

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

To Find :     The average force acting on plate

Solution:

Bullets of  40g mass each hit a plate at the rate of 100 bullet per second,

=> mass per second    40 * 100  = 4000 g  = 4 kg

Hot with a velocity  = 60 m/s

Reflect back with velocity = 30 m/s

Hence Velocity = - 30 m/s   as  direction is reversed

Change in momentum  =  4 (60 - (-30))  = 360  kgm/s

The average force acting on plate is = Rate of change of momentum

Time = 1 sec

=  360/1

= 360N

. The average force acting on plate is 360  N

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Answer 2

Given:

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

To find:

Average force on the plate?

Calculation:

• Force is defined as the rate of change of momentum with respect to time.

Now, first of all, let's calculate momentum change:

$\sf\Delta P = m(\Delta v)$

$\sf \implies\Delta P = \dfrac{40}{1000} \{60 -(- 30)\}$

$\sf \implies\Delta P = \dfrac{40}{1000} (90)$

$\sf \implies\Delta P = 3.6 \: kg \: m/s$

Now, force be F :

$\sf \implies F = \dfrac{n \times \Delta P}{t}$

• 'n' refers to number of bullets.

$\sf \implies F = \dfrac{100\times 3.6}{1}$

$\sf \implies F = 360\: N$

So, force on plate is 360 N.