a 2.5 kg rifle fires a 20 g bullet at 400 m/s. What is the magnitude of the recoil velocity of the rifle?
Try using conservation of momentum.
recoil momentum and bullet momentum are equal and opposite, so that the sum is zero.
3,2
To find the magnitude of the recoil velocity of the rifle, we can use the principle of conservation of momentum.
According to the principle of conservation of momentum, the total momentum before the bullet is fired is equal to the total momentum after the bullet is fired. In this case, the rifle and the bullet form a closed system.
The initial momentum of the closed system is zero since the rifle is initially at rest. After the bullet is fired, the bullet and the rifle move in opposite directions. Let's assume the recoil velocity of the rifle is v.
To calculate the momentum of the bullet, we multiply its mass (20 g = 0.02 kg) by its velocity (400 m/s):
Momentum of the bullet = mass of bullet × velocity of bullet
= 0.02 kg × 400 m/s
= 8 kg·m/s
Since the total momentum before the bullet is fired is zero, the total momentum after the bullet is fired should also be zero. Therefore, the momentum of the rifle is equal to the negative momentum of the bullet:
Momentum of the rifle = - Momentum of the bullet
= - 8 kg·m/s
Now we can calculate the magnitude of the recoil velocity of the rifle using the formula for momentum:
Momentum = mass × velocity
Since the mass of the rifle is given as 2.5 kg, we can rearrange the equation to solve for velocity:
Velocity = Momentum / mass
Substituting the values:
Velocity = - 8 kg·m/s / 2.5 kg
= - 3.2 m/s
The negative sign indicates that the rifle moves in the opposite direction as the bullet. To find the magnitude, we take the absolute value of the recoil velocity:
Magnitude of the recoil velocity = |-3.2 m/s|
= 3.2 m/s
Therefore, the magnitude of the recoil velocity of the rifle is 3.2 m/s.