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
To calculate the speed with which the gun recoils when the bullet is fired, we can use the principle of conservation of momentum. According to this principle, the total momentum of an isolated system remains constant before and after an event.
In this case, the isolated system consists of the bullet and the gun. Initially, the system is at rest. When the bullet is fired, it gains momentum in one direction, and as a result, the gun recoils in the opposite direction to conserve the overall momentum.
The momentum of an object is given by the equation: momentum (p) = mass (m) × velocity (v).
Let's consider the bullet's initial momentum (p1) and the gun's initial momentum (p2):
p1 = m1 × v1
p2 = m2 × v2
Here, m1 represents the mass of the bullet, m2 represents the mass of the gun, v1 represents the initial velocity of the bullet, and v2 represents the final velocity of the gun.
Since the bullet is fired, its final velocity (v1) becomes zero, and the final velocity of the gun (v2) is what we need to calculate.
Due to the conservation of momentum, the total momentum before and after the event remains the same:
0 = p1 + p2
Given:
m1 = 0.01 kg (mass of the bullet)
m2 = 5.0 kg (mass of the gun)
v1 = 250 m/s (initial velocity of the bullet)
v2 = ? (final velocity of the gun)
Now, let's substitute the values into the equation and solve for v2:
0 = (0.01 kg) × 0 + (5.0 kg) × v2
0 = 0 + 5.0 kg × v2
0 = 5.0 kg × v2
v2 = 0 m/s
Therefore, the final velocity of the gun (v2) is zero. The gun recoils with zero speed or remains at rest due to the bullet's recoil.
momentum relation:
mb*vb+Mg*Vg=0
vg= - mb*vb/Mg
and speed is the absolute value of velociyt.