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?
I still don't understand. Could you please help with a formula? Thank you.
physics - drwls, Monday, February 7, 2011 at 6:38pm
Try using conservation of momentum.
recoil momentum and bullet momentum are equal and opposite, so that the sum is zero.
Sure! The formula you can use is the principle of conservation of momentum, which states that the total momentum before an event is equal to the total momentum after the event.
In this case, the total momentum before firing the rifle is zero, since the rifle is initially at rest. After firing the rifle, the total momentum should still be zero, but now it will be divided between the bullet and the recoiling rifle.
The formula for momentum (p) is:
p = mv
where m is the mass and v is the velocity.
So, the momentum of the bullet after firing is:
pb = (mass of the bullet) x (velocity of the bullet)
And the momentum of the recoiling rifle is:
pr = (mass of the rifle) x (velocity of the rifle)
According to the conservation of momentum, pb + pr = 0.
We are given the mass of the bullet (20 g) and the velocity of the bullet (400 m/s). We are also given the mass of the rifle (2.5 kg).
To find the recoil velocity of the rifle, we can rearrange the equation:
pr = -pb , where pr and pb are the magnitudes of the momenta.
Therefore,
(mass of the rifle) x (velocity of the rifle) = -(mass of the bullet) x (velocity of the bullet)
Substituting the given values,
(2.5 kg) x (velocity of the rifle) = -(0.020 kg) x (400 m/s)
Now, you can solve for the velocity of the rifle.
To find the magnitude of the recoil velocity of the rifle, you can use the principle of conservation of momentum. According to this principle, the total momentum before an event is equal to the total momentum after the event, provided no external forces are acting on the system.
In this case, the rifle and the bullet are the system. The rifle is initially at rest, so its momentum is zero. The bullet has a mass of 20 g, which is 0.02 kg, and a velocity of 400 m/s.
To find the magnitude of the recoil velocity of the rifle, we can use the following formula:
(mass of rifle) × (recoil velocity) = (mass of bullet) × (bullet velocity)
Substituting the given values:
(2.5 kg) × (recoil velocity) = (0.02 kg) × (400 m/s)
Now we can solve for the recoil velocity:
(recoil velocity) = (0.02 kg) × (400 m/s) / (2.5 kg)
(recoil velocity) = 0.32 m/s
So the magnitude of the recoil velocity of the rifle is 0.32 m/s.