A bullet of mass 0.045kg is fired from a gun of mass9kg, the bullet moving with an initial velocity of 200ms. Find the initial recall of the gun
To find the initial recoil of the gun, we can use the law of conservation of momentum. According to this law, the total momentum before the bullet is fired should be equal to the total momentum after the bullet is fired.
The momentum of an object can be calculated by multiplying its mass by its velocity. Therefore, we can calculate the momentum of the bullet and the gun before and after the bullet is fired.
Before the bullet is fired, the gun and the bullet are at rest, so their momenta are both zero.
Total initial momentum = Momentum of bullet + Momentum of gun = 0 + 0 = 0
After the bullet is fired, the bullet and the gun will have opposite momenta. Let's say the recoil velocity of the gun is v.
The momentum of the bullet can be calculated as:
Momentum of bullet = mass of bullet * velocity of bullet
The momentum of the gun can be calculated as:
Momentum of gun = mass of gun * recoil velocity of gun
According to the law of conservation of momentum, the total momentum before and after the firing should be the same. So we can set up the following equation:
Total initial momentum = Total final momentum
0 = (mass of bullet * velocity of bullet) + (mass of gun * recoil velocity of gun)
Now, let's substitute the given values into the equation:
0 = (0.045 kg * 200 m/s) + (9 kg * recoil velocity of gun)
Simplifying the equation:
0 = 9.0 kg * recoil velocity of gun + 9.0 kg * recoil velocity of gun
0 = 18.0 kg * recoil velocity of gun
To find the recoil velocity of the gun, we can rearrange the equation:
recoil velocity of gun = 0 / 18.0 kg
recoil velocity of gun = 0 m/s
Therefore, the initial recall velocity of the gun is 0 m/s. This means that the gun does not move backward when the bullet is fired.