A rifle with a mass of 0.9 fires a bullet with a mass of 6.0 g (0.006 kg). The bullet moves with a muzzle velocity of 750 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 if the recoil velocity of the rifle?
m v = .006 * 750
0.9 u + .006 * 750 = 0 since there was zero momentum before you pulled the trigger.
u = -.006*750/0.9
A. To answer question A, we need to calculate the momentum of the bullet after the rifle is fired. The momentum of an object is given by the product of its mass and velocity.
The mass of the bullet is given as 0.006 kg, and the muzzle velocity is given as 750 m/s. Therefore, the momentum of the bullet can be calculated as follows:
Momentum = Mass x Velocity
= 0.006 kg x 750 m/s
= 4.5 kg·m/s
So, the momentum of the bullet after the rifle is fired is 4.5 kg·m/s.
B. Now, let's move on to question B where we need to calculate the recoil velocity of the rifle. The law of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, as long as there are no external forces involved.
The initial momentum of the system (rifle + bullet) is zero, as the rifle and bullet are initially at rest. The final momentum of the system should also be zero, as there are no external forces acting on the rifle.
Therefore, we can say:
Initial momentum = Final momentum
Momentum of rifle + Momentum of bullet = 0
The momentum of the rifle can be calculated as:
Momentum of rifle = - (Momentum of bullet)
Plugging in the value calculated in question A, we have:
Momentum of rifle = -4.5 kg·m/s
Since the rifle has a mass of 0.9 kg, we can calculate the recoil velocity using the equation:
Momentum = Mass x Velocity
-4.5 kg·m/s = 0.9 kg x Velocity
Solving for Velocity, we get:
Velocity = -4.5 kg·m/s / 0.9 kg
= -5 m/s
Therefore, the recoil velocity of the rifle after the bullet is fired is -5 m/s. The negative sign indicates that the rifle moves in the opposite direction to that of the bullet.
A. To find the momentum of the bullet after the rifle is fired, we can use the formula:
Momentum = mass × velocity
Given:
Mass of the bullet (m) = 0.006 kg
Velocity of the bullet (v) = 750 m/s
Using the formula, we can calculate the momentum:
Momentum = 0.006 kg × 750 m/s
Momentum = 4.5 kg⋅m/s
Therefore, the momentum of the bullet after the rifle is fired is 4.5 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 of a system remains constant unless acted upon by external forces. In this case, we can assume that the system consists of the bullet and the rifle.
According to conservation of momentum:
Initial momentum of the system = Final momentum of the system
Initially, the rifle is at rest, so the initial momentum of the system is zero. The final momentum of the system is the sum of the momentum of the bullet and the rifle.
Momentum of the system = Momentum of the bullet + Momentum of the rifle
0 = (mass of the bullet × velocity of the bullet) + (mass of the rifle × recoil velocity of the rifle)
0 = (0.006 kg × 750 m/s) + (0.9 kg × recoil velocity of the rifle)
Simplifying the equation:
0 = 4.5 kg⋅m/s + (0.9 kg × recoil velocity of the rifle)
Rearranging the equation to solve for the recoil velocity of the rifle:
Recoil velocity of the rifle = - (4.5 kg⋅m/s) / (0.9 kg)
Recoil velocity of the rifle = - 5 m/s (rounded to the nearest meter per second)
Therefore, if external forces acting on the rifle can be ignored, the recoil velocity of the rifle is -5 m/s. The negative sign indicates that the rifle moves in the opposite direction to the bullet's movement.