A 100g bullet is firred from a 10 kg gun with a speed of 1000 m/s.What is the speed of recoil of the gun.
0=m1v1+MV
MV=-mv
V=-mv/M
=O.1×1000/10
v=-10m/s
why negative sign?
To find the speed of recoil of the gun, we can make use of the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired must be equal to the total momentum after the bullet is fired.
The momentum of an object is calculated by multiplying its mass with its velocity. Let's assume the speed of recoil of the gun is v (in m/s).
Before firing the bullet, the total momentum is given by the sum of the gun's momentum and the bullet's momentum. The momentum of the gun is calculated as the product of its mass (10 kg) and its initial velocity (0 m/s because it was initially at rest).
Total momentum before firing = (gun's momentum) + (bullet's momentum)
= (10 kg) x (0 m/s) + (0.1 kg) x (1000 m/s)
= 0 kg*m/s + 100 kg*m/s
= 100 kg*m/s
After firing the bullet, the total momentum is given by the sum of the gun's momentum (now in the opposite direction) and the bullet's momentum (now moving forward with a speed of 1000 m/s).
Total momentum after firing = (gun's momentum) + (bullet's momentum)
= (10 kg) x (-v m/s) + (0.1 kg) x (1000 m/s)
= -10v kg*m/s + 100 kg*m/s
= (100 - 10v) kg*m/s
Since the total momentum before and after firing must remain the same, we equate the two expressions:
100 kg*m/s = (100 - 10v) kg*m/s
To solve for v, let's isolate v on one side of the equation:
100 - 10v = 100
-10v = 0
v = 0 m/s
Therefore, the speed of recoil of the gun is 0 m/s. This means the gun does not move backward when the bullet is fired.