Final answer:
To find the average force exerted on the hunter's shoulder by the rifle, we must know the mass and velocity of the rifle or bullet. Using the work-energy principle and the conservation of momentum, we can calculate the kinetic energy of the rifle and then divide it by the stopping distance to get the average force.
Step-by-step explanation:
To calculate the magnitude of the average force exerted on the hunter's shoulder by the rifle, we can use the work-energy principle which states that the work done by the forces on the rifle is equal to the change in kinetic energy. In this case, the work done by the force to stop the rifle is going to be the negative of the kinetic energy the rifle had initially.
The formula to find the work is:
Work = Force × Distance
And the kinetic energy (KE) of the rifle is given by:
KE = ½×m×v2
So, if the rifle initially had the same momentum as the bullet, which means:
Momentum (p) = mass of bullet (mb) × velocity of bullet (vb)
Momentum conservation implies that the rifle will have a velocity (vr) such that:
p = mass of rifle (mr) × vr
Thus, vr = mb × vb / mr
Since there's no initial information about the mass and velocity of the rifle or bullet, to solve for the force, we would need the rifle's mass and initial velocity or the bullet's mass and velocity. Assuming we know these values, we can then calculate the average force exerted on the shoulder using:
Average Force (F) = - KE / Distance
Bear in mind, the force should be considered to be average because it is not necessarily applied uniformly over the stopping distance.