A rifle has a mass of 4.73 kg and it fires a bullet of mass 13.6 g at a muzzle speed of 829 m/s. What is the recoil speed of the rifle as the bullet leaves the gun barrel?
So far, I've got (using p for momentum) p=p, so massXchange in velocity of the bullet will will equal the massXchange in velocity of the rifle. So my work looks like:
.136kg x 829m/s = 4.73kg x v
Which gives me 23.8m/s, which is incorrect. What am I doing wrong?
For speed, it is correct. If it were asking for velocity, I would add a negative sign, meaning the opposite direction from the bullet.
I've tried that, but the program I'm using still says that that is incorrect.
The program is incorrect. Put a hex on it.
is there .136kg for 13.6g.....check that
13.6g is 0.0136kg
2.09m/s
In order to find the recoil speed of the rifle, we can apply the conservation of momentum principle. You are on the right track by equating the final momentum of the bullet to the initial momentum of the rifle.
However, there is a small mistake in your calculation. The mass of the bullet should be converted to kilograms before calculation. 13.6 g is equal to 0.0136 kg, not 0.136 kg.
Let's correct it and calculate the recoil speed of the rifle again:
Bullet mass: 0.0136 kg
Bullet velocity: 829 m/s
Rifle mass: 4.73 kg
Recoil velocity of the rifle: v (unknown)
Using the conservation of momentum:
Initial momentum of the system (before firing) = Final momentum of the system (after firing)
Initial momentum of the system = 0 (since the rifle is initially at rest)
Final momentum of the system = (mass of the bullet) × (velocity of the bullet) + (mass of the rifle) × (recoil velocity of the rifle)
Equation: 0 = (0.0136 kg) × (829 m/s) + (4.73 kg) × (v)
Now we can solve for v, the recoil velocity of the rifle:
0 = 0.0136 kg × 829 m/s + 4.73 kg × v
Rearranging the equation:
- (0.0136 kg × 829 m/s) = 4.73 kg × v
Solving for v:
v = - (0.0136 kg × 829 m/s) / 4.73 kg
v = -11.8828 m/s
The negative sign indicates that the recoil velocity is in the opposite direction to the bullet's velocity. Therefore, the recoil speed of the rifle as the bullet leaves the gun barrel is approximately 11.8828 m/s.