If the rifle is stopped by the hunter’s shoulder in a distance of 3.16 cm, what is the magnitude of the average force exerted on the shoulder by the rifle?
Answer in units of N.
mass of bullet= 0.0137 kg
velocity of bullet= 546 m/s to the right
mass of rifle= 3.82 kg
recoil speed of the rifle as the bullet leaves the rifle= 1.958167539 m/s
1. Change the distance from cm to meters by dividing by 100.
3.16cm -> 0.0316m
2. Use this formula to find time.
t= 2(x-displacement-)/V(speed)
2 • 0.0316m/1.958167539 = 0.032275s
3. Use this formula for Force F=mv/t
3.82kg • 1.958167539/ 0.032275 = 231.765N
The answer is 231.765N
To find the magnitude of the average force exerted on the shoulder by the rifle, we can use the principle of conservation of momentum.
The principle of conservation of momentum states that the total momentum before an event is equal to the total momentum after the event, as long as no external forces are acting on the system.
In this case, the system consists of the bullet and the rifle, with the hunter's shoulder acting as the external force. Initially, the bullet and the rifle are at rest, so their total momentum is zero. After the bullet is fired, the bullet moves to the right with a certain velocity, and the rifle recoils to the left with a certain velocity.
We can calculate the momentum of the bullet before and after the event using the equation:
Momentum = mass * velocity
Before the event:
Momentum of the bullet = mass of bullet * velocity of bullet = 0.0137 kg * 546 m/s = 7.4912 kg*m/s (to the right)
After the event:
Momentum of the bullet = 0 (since it comes to rest after the event)
Now, using the principle of conservation of momentum, we can find the recoil velocity of the rifle:
Total initial momentum = Total final momentum
(0.0137 kg * 546 m/s) + (3.82 kg * 0 m/s) = 0 + (3.82 kg * recoil velocity of the rifle)
Rearranging the equation and solving for the recoil velocity of the rifle:
Recoil velocity of the rifle = [(0.0137 kg * 546 m/s) + (3.82 kg * 0 m/s)] / 3.82 kg
Recoil velocity of the rifle ≈ 0.0216 m/s (to the left)
Now, to find the force exerted on the shoulder by the rifle, we can use Newton's second law of motion:
Force = mass * acceleration
Since the rifle is recoiling with a constant velocity, the acceleration is zero, and hence the force exerted on the shoulder by the rifle is also zero.
Therefore, the magnitude of the average force exerted on the shoulder by the rifle is 0 N.