A machine gun of mass 10 kg fires 20g bullets at the rate of 10 bullets per second, with the speed of 500 m/s. What is the force necessary to hold the gun in position?
100N
To find the force necessary to hold the gun in position, we need to consider the principle of action and reaction, also known as Newton's third law of motion. According to Newton's third law, for every action, there is an equal but opposite reaction.
In this case, when the machine gun fires a bullet, an equal and opposite recoil force is exerted on the gun. This recoil force is responsible for pushing the gun backward, and we need to calculate its magnitude.
First, we need to determine the momentum of each bullet fired by the machine gun. Momentum (p) is defined as the product of an object's mass (m) and its velocity (v). In this case, the mass of each bullet is 20g, which is equivalent to 0.02 kg, and the velocity of each bullet is 500 m/s.
So, the momentum of each bullet is given by:
p = m * v = 0.02 kg * 500 m/s = 10 kg·m/s
Since the machine gun fires 10 bullets per second, the total momentum change per second is:
total momentum change = 10 bullets/second * 10 kg·m/s = 100 kg·m/s per second
According to Newton's third law, the recoil force exerted on the gun is equal in magnitude but opposite in direction to the total momentum change per second. Therefore, the force necessary to hold the gun in position is:
force = total momentum change / time
Given that the total momentum change per second is 100 kg·m/s per second, and the time interval is 1 second (since the machine gun fires 10 bullets per second), we can calculate the force as:
force = 100 kg·m/s per second / 1 second
force = 100 kg·m/s²
Therefore, the force necessary to hold the gun in position is 100 Newtons (N).