A bullet of mass 20g is fired from a rifle of mass 4kg with a speed of 500ms^-1.Calculate the initial velocity of the recoil of the rifle.
Conservation of momentum. Zero = zero.
To calculate the initial velocity of the recoil of the rifle, we can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this case, we have a bullet and a rifle, which can be considered as a system. Before the bullet is fired, both the bullet and the rifle are at rest, so their initial momentum is zero.
The momentum of an object can be calculated using the formula:
momentum = mass × velocity
The final momentum of the system can be calculated by considering the bullet and the rifle separately. Let's assume the final velocity of the bullet is v_bullet, and the final velocity of the rifle is v_rifle.
The final momentum of the bullet is:
momentum_bullet = mass_bullet × v_bullet
The final momentum of the rifle is:
momentum_rifle = mass_rifle × v_rifle
According to the conservation of momentum, the total initial momentum (which is zero) is equal to the total final momentum:
0 = momentum_bullet + momentum_rifle
Substituting the given values, we have:
0 = (mass_bullet × v_bullet) + (mass_rifle × v_rifle)
We can rearrange this equation to solve for the initial velocity of the rifle (v_rifle):
v_rifle = -(mass_bullet / mass_rifle) × v_bullet
Plugging in the values, we get:
v_rifle = -(0.020 kg / 4 kg) × 500 m/s
Simplifying further, we have:
v_rifle = -0.01 × 500 m/s
v_rifle = -5 m/s
Therefore, the initial velocity of the recoil of the rifle is -5 m/s. The negative sign indicates that the rifle moves in the opposite direction to the bullet.