a 3.5kg rifle fires a 5gram bullet with a muzzle speed of 300m/s. What is the recoil speed of the rifle?
52.5
0.4
To calculate the recoil speed of the rifle, we can use the principle of conservation of momentum. According to this principle, the total momentum before the bullet is fired is 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. In this case, the momentum of the rifle before firing is given by:
Momentum of rifle before firing = mass of rifle × velocity of rifle before firing
Similarly, the momentum of the bullet after being fired is given by:
Momentum of bullet after firing = mass of bullet × velocity of bullet after firing
Since the bullet is fired in one direction, the momentum of the bullet is equal in magnitude but opposite in direction to the recoil momentum of the rifle, given by:
Recoil momentum of rifle = -momentum of bullet after firing
Now, let's calculate the recoil speed of the rifle.
Mass of the rifle (m_rifle) = 3.5 kg
Velocity of the rifle before firing (v_rifle) = 0 m/s (since it's initially at rest)
Mass of the bullet (m_bullet) = 5 g = 0.005 kg
Velocity of the bullet after firing (v_bullet) = 300 m/s
Using the equations mentioned earlier, we can calculate the momentum of the rifle before firing and the momentum of the bullet after firing:
Momentum of rifle before firing = m_rifle × v_rifle
Momentum of bullet after firing = m_bullet × v_bullet
Next, to calculate the recoil speed of the rifle, we need to find the recoil momentum of the rifle, which is equal in magnitude but opposite in direction to the momentum of the bullet after firing:
Recoil momentum of rifle = - momentum of bullet after firing
Finally, to determine the recoil speed, we divide the recoil momentum by the mass of the rifle and take the absolute value:
Recoil speed of the rifle = |Recoil momentum of rifle| / mass of the rifle
Now let's substitute the values and calculate the recoil speed of the rifle:
Momentum of rifle before firing = 3.5 kg × 0 m/s = 0 kg·m/s
Momentum of bullet after firing = 0.005 kg × 300 m/s = 1.5 kg·m/s
Recoil momentum of rifle = -1.5 kg·m/s (since the bullet and rifle have equal magnitudes but opposite directions)
Recoil speed of the rifle = |Recoil momentum of rifle| / mass of the rifle
Recoil speed of the rifle = | -1.5 kg·m/s | / 3.5 kg = 0.43 m/s (rounded to two decimal places)
Therefore, the recoil speed of the rifle is approximately 0.43 m/s.