Recoil Speed Calculation using Conservation of Momentum
This problem involves calculating the recoil speed of a gun when a bullet is fired from it. We can solve this using the principle of conservation of linear momentum.
Principle: The total momentum of a system remains constant if no external forces act upon it. In this case, before firing, the gun and bullet are at rest, so the initial momentum is zero. After firing, the momentum of the bullet and the gun must sum to zero.
Given Data:
- Mass of bullet ($m_b$) = $10 \ g = 0.01 \ kg$
- Velocity of bullet ($v_b$) = $100 \ m/s$
- Mass of gun ($m_g$) = $1 \ kg$
- Recoil speed of gun ($v_g$) = ?
Conservation of Momentum Equation
According to the conservation of momentum:
$m_b v_b + m_g v_g = 0$We need to find the recoil speed ($v_g$). Rearranging the equation:
$v_g = - \frac{m_b v_b}{m_g}$Calculating Recoil Speed
Substitute the given values into the equation:
$v_g = - \frac{(0.01 \ kg) \times (100 \ m/s)}{1 \ kg}$ $v_g = - \frac{1 \ kg \cdot m/s}{1 \ kg}$ $v_g = -1 \ m/s$The negative sign indicates that the gun moves in the opposite direction to the bullet. The recoil speed is the magnitude of this velocity.
Recoil speed = $|v_g| = |-1 \ m/s| = 1 \ m/s$.
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