A Gun of Mass 3.5kg fires a bullet at 320m/s. If the gun recoils with a speed of 24m/s, calculate the mass of the bullet.
conserve momentum
3.5*24 = m*320
To calculate the mass of the bullet, we can use the principle of conservation of momentum. According to this principle, the total momentum before the firing is equal to the total momentum after the firing.
Let's assume the mass of the bullet is 'm'. We know the mass of the gun is 3.5kg, and it recoils with a velocity of 24m/s. The bullet is fired with a velocity of 320m/s.
The momentum of an object is calculated by multiplying its mass with its velocity. Therefore, the momentum of the gun before the firing is given by:
Momentum of the gun before firing = Mass of the gun * Velocity of the gun
= 3.5 kg * 0m/s (since the gun is initially at rest)
The momentum of the bullet is given by:
Momentum of the bullet = Mass of the bullet * Velocity of the bullet
= m kg * 320m/s
The momentum of the gun after firing is given by:
Momentum of the gun after firing = Mass of the gun * Recoil velocity of the gun
= 3.5kg * (-24m/s) (negative value since the gun moves in the opposite direction)
According to the principle of conservation of momentum, the total momentum before the firing should be equal to the total momentum after the firing. Therefore:
Momentum of the gun before firing + Momentum of the bullet = Momentum of the gun after firing
Substituting the given values, we have:
0 + m kg * 320m/s = 3.5kg * (-24m/s)
Simplifying the equation:
320m/s * m = 3.5kg * (-24m/s)
320m * m = -84kg * m/s
Dividing both sides by 320m:
m = (-84kg * m/s) / 320m
m = -0.2625kg
The mass of the bullet is approximately 0.2625 kilograms.