a bullet of mass 0.01kg is fired from a gun weighing 5.0kg . If the initial speed of bullet is 250 m/sec, calculate the speed with which the gun recoils
.05 m/sec
To calculate the speed with which the gun recoils, we can use the principle of conservation of momentum. According to this principle, the total momentum of a system remains constant if no external forces are acting on it.
The initial momentum of the system is given by the sum of the momentum of the bullet and the momentum of the gun before firing:
Initial momentum = (mass of bullet * velocity of bullet) + (mass of gun * velocity of gun)
Final momentum of the system is the sum of the momentum of the bullet and the momentum of the gun after firing:
Final momentum = (mass of bullet * final velocity of bullet) + (mass of gun * final velocity of gun)
Since there are no external forces acting on the system, the initial and final momentum are equal:
Initial momentum = Final momentum
In this case, the initial momentum of the system is 0 since the gun is at rest initially. Therefore, the final momentum of the system is 0 as well.
We can set up the equation as follows:
0 = (0.01 kg * final velocity of bullet) + (5 kg * final velocity of gun)
Now we can solve for the final velocity of the gun:
0 = (0.01 kg * 250 m/s) + (5 kg * final velocity of gun)
0 = 2.5 + (5 kg * final velocity of gun)
-2.5 = 5 kg * final velocity of gun
final velocity of gun = -2.5 kg / 5 kg
final velocity of gun = -0.5 m/s
So, the speed with which the gun recoils is 0.5 m/s in the opposite direction to the bullet's motion.