A 4.1 kg rifle is suspended by strings and fires a 0.0030 kg bullet at a speed of 1500
m/s. What is its recoil speed in m/s?
To find the recoil speed of the rifle, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired.
The momentum is defined as the product of an object's mass and velocity:
Momentum (p) = mass (m) x velocity (v)
Before the bullet is fired, the rifle is at rest, so its velocity is 0 m/s. The total momentum before firing is therefore 0 kg•m/s, since the rifle has no momentum.
After the bullet is fired, the momentum of the bullet is given by:
p_bullet = m_bullet * v_bullet
where m_bullet is the mass of the bullet (0.0030 kg) and v_bullet is the velocity of the bullet (1500 m/s).
Since the total momentum before firing is equal to the total momentum after firing, we can write:
0 kg•m/s = (m_rifle + m_bullet) * v_recoil
where m_rifle is the mass of the rifle (4.1 kg) and v_recoil is the recoil speed of the rifle that we need to find.
Rearranging the equation, we can solve for v_recoil:
v_recoil = - (m_bullet * v_bullet) / m_rifle
Plugging in the values, we get:
v_recoil = - (0.0030 kg * 1500 m/s) / 4.1 kg
Calculating this expression, we find that the recoil speed of the rifle is approximately -13.41 m/s.
Note: The negative sign indicates that the direction of the recoil speed is opposite to that of the bullet's velocity.