Question

What change will a force bring in a body? From a rifle of mass \[5kg\] , a bullet of mass \[50g\] is fired with an initial velocity of \[50m/s\] . Calculate initial recoil velocity of the rifle. Explain how Newton's second law of motion is used in sports?

Answer 1

Hint: The property of law of conservation of momentum is used here. Using the law of conservation of momentum, we can find the recoil velocity of the given rifle. Moving to the second part of the question, we can approach this by stating Newton's second law and applying it to some sports.

Formula used: According to the law of conservation of momentum, momentum before collision is equal to momentum after collision.
\[{P_f} = {m_g}{v_g} + {m_b}{v_b}\]
Where, \[{m_g}\] is the mass of the gun
\[{v_g}\] is the velocity of the gun
\[{m_b}\] is the mass of the bullet and,
\[{v_b}\] is the velocity of the bullet

Complete step by step solution:
The following data is given,
Mass of the gun, \[{m_g} = 5kg\]
Mass of the bullet, \[{m_b} = 50g\]
Velocity of the bullet, \[{v_b} = 50m/s\]
Let us start by stating the law of conservation of momentum. It states that, momentum before collision is equal to momentum after collision.
We are asked to find the recoil velocity, here we take it as the velocity of the gun.
In order to find the recoil velocity or the velocity of the gun, we separate the value in the equation,
  \[{P_f} = {m_g}{v_g} + {m_b}{v_b}\]
Taking the value to be found to one side, we have,
\[{v_g} = \dfrac{{P - {m_b}{v_b}}}{{{m_g}}}\]
Now we substitute the corresponding value to the equation above,
\[{v_g} = \dfrac{{0 - 0.050 \times 50}}{{5kg}} = - 0.5m/s\]
The final momentum is zero because the motion of the bullet is stopped as it comes to rest.
Hence, the initial recoil velocity of the rifle is \[ - 0.5m/s\]

Newton's second law states that, the rate of change of momentum of a body is directly proportional to the force applied to it.
Taking an example to show how the law is applicable in sports, a fielder in the sport of cricket often pulls his hand backward which allows the acceleration of the bullet to decrease which makes the effect of force on his hand less which hurts lesser than it would if he does not pull his hand backward.

Note:
The value of recoil velocity is found out to have a negative value. This is because the motion of the gun is in the opposite direction of motion of the bullet. We must know the applications of laws of motion in the numericals in order to get to the final answer of this problem. Calculations must be taken care of while solving numericals.