A rifle with a mass of 1.84 kg fires a bullet with a mass of 4.5 g (0.0045 kg). The bullet moves with a muzzle velocity of 413 m/s after the rifle is fired.
(a) What is the momentum of the bullet after the rifle is fired?
(b) If external forces acting on the rifle can be ignored, what is the recoil velocity of the rifle?
A.)p = m * v
With the bullet travelling at v =413 m/s with a mass of 0.0045 kg:
p(bullet) = 0.0045 * 413
p(bullet) = 1. 8585 N.s
answer: 1.8585 N.s
B.)The recoil velocity of the rifle, this is a conservation of momentum problem. So,
p(initial) = p(final)
In other words, the products of all masses with their velocities should be equal before and after the interaction. This becomes:
m1*u1 + m2*u2 = m1*v1 + m2*v2 :
(1.884)(0) + (0.0045)(0) = (1.84) v1 + (0.0045)(413)
0 = 1.84 * v1 + 1.8585
-1.8585 = 1.84 * v1
v1 = -1.8585 / 1.84
v1 = -1.010054348 m/s
answer: 1.010054348 m/s
To find the momentum of the bullet after the rifle is fired, we can use the formula:
Momentum = mass × velocity
(a) The mass of the bullet is 0.0045 kg, and the velocity is 413 m/s. Plugging these values into the formula, we have:
Momentum of the bullet = 0.0045 kg × 413 m/s = 1.8585 kg·m/s
So, the momentum of the bullet after the rifle is fired is approximately 1.8585 kg·m/s.
(b) To find the recoil velocity of the rifle, we can use 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, before the rifle is fired, the total momentum is zero since the rifle and bullet are initially at rest. After the rifle is fired, the momentum of the bullet is 1.8585 kg·m/s (as calculated in part (a)).
Since the total momentum before and after must be the same, the momentum of the rifle after firing must also be 1.8585 kg·m/s in the opposite direction.
Now, to find the recoil velocity of the rifle, we use the formula:
Momentum = mass × velocity
Given that the mass of the rifle is 1.84 kg, we can rearrange the formula to solve for velocity:
Velocity of the rifle = Momentum of the rifle / Mass of the rifle
Substituting the values, we have:
Velocity of the rifle = 1.8585 kg·m/s / 1.84 kg ≈ 1.01 m/s
Therefore, the recoil velocity of the rifle is approximately 1.01 m/s in the opposite direction of the bullet.