a bullet of mass 0.01kg is fired from a gun weighting 5 kg. If the initial speed of the bullet is-250 m/sec, calculate the speed with which the gun recoils
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To calculate the speed with which the gun recoils, we can apply the principle of conservation of momentum. Conservation of momentum states that the total momentum of a system remains constant before and after an event, as long as no external forces are acting on the system.
In this case, the bullet and the gun are the system, and the initial momentum of the system is zero because both the bullet and the gun are initially at rest. After the bullet is fired, it acquires momentum in the forward direction, and the gun acquires momentum in the opposite direction to maintain the total momentum at zero.
Now, let's proceed with the calculations:
1. Calculate the momentum of the bullet:
Momentum = mass × velocity
Momentum = 0.01 kg × (-250 m/s)
Momentum = -2.5 kg·m/s (Note: The negative sign indicates the direction is opposite to the initial state)
2. Apply conservation of momentum to find the gun's recoil velocity:
Initial momentum of the system = Final momentum of the system
0 = (mass of bullet × velocity of bullet) + (mass of gun × velocity of gun)
0 = (0.01 kg × (-250 m/s)) + (5 kg × velocity of gun)
Rearrange the equation to solve for the velocity of the gun:
0.01 kg × (-250 m/s) = -5 kg × velocity of gun
velocity of gun = (0.01 kg × (-250 m/s)) / (-5 kg)
velocity of gun ≈ 0.5 m/s (rounded to the nearest decimal place)
Therefore, the gun recoils with a velocity of approximately 0.5 m/s in the opposite direction to the bullet.