A bullet with mass 0.40 kg is fired with an initial velocity of 400 m/s from a gun with mass 5.0 kg. The speed of the reoil of the gun is?
Do I have to 0.40 and 5.0 an then divide that by 400?
No. The bullet's momentum (0.40)x400 equals the recoiling gun's momentum (in the opposite direction.
That makes the recoil velocity 0.40*400/5.0
No, you do not need to divide the masses of the bullet and the gun by the initial velocity. Instead, to find the speed of the recoil of the gun, you 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.
First, let's find the initial momentum of the system (bullet + gun) before the bullet is fired. The momentum (p) is equal to mass (m) multiplied by velocity (v). The initial momentum of the bullet is given by:
Momentum of the bullet = mass of the bullet x initial velocity of the bullet
= 0.40 kg x 400 m/s
The initial momentum of the gun is given by:
Momentum of the gun = mass of the gun x initial velocity of the gun
= 5.0 kg x 0 m/s (as the gun is initially at rest before being fired)
Now, let's find the total momentum after the bullet is fired. The bullet is moving with a certain velocity (let's call it Vb) after being fired, and the gun recoils with a certain velocity (let's call it Vg).
The total momentum after the bullet is fired is:
Total momentum = (mass of the bullet x final velocity of the bullet) + (mass of the gun x final velocity of the gun)
Since the final velocity of the bullet is given as 400 m/s (assuming it is not slowed down or accelerated after being fired), we can write:
Total momentum = (0.40 kg x 400 m/s) + (5.0 kg x final velocity of the gun)
According to the conservation of momentum, the total momentum before and after the bullet is fired is equal:
Initial momentum = Total momentum
Therefore, we can equate the initial momentum with the total momentum equation above and solve for the final velocity of the gun:
(Momentum of the bullet) + (Momentum of the gun) = (Momentum of the bullet) + (Momentum of the gun)
Substituting the values we have:
(0.40 kg x 400 m/s) + (5.0 kg x 0 m/s) = (0.40 kg x 400 m/s) + (5.0 kg x final velocity of the gun)
Simplifying the equation, we get:
(0.40 kg x 400 m/s) = (5.0 kg x final velocity of the gun)
Finally, divide both sides by 5.0 kg to solve for the final velocity of the gun:
Final velocity of the gun = (0.40 kg x 400 m/s) / 5.0 kg
Calculating the above expression will give you the speed of the recoil of the gun.