Dynamics: Newton's 2nd Law

Question

What average net force is required to accelerate a 8.7 g bullet from rest to 700 m/s over a distance of 0.78 m along the barrel of a rifle? 

Answer 1

There are two methods with which you can solve this problem:

1) Kinematics

The problem provides you with both the initial velocity (rest) and the final velocity. It also provides the distance over which the bullet accelerates. Using the appropriate equation, you can solve for the acceleration the bullet undergoes. The final step is to use Newton's 2nd Law equation (F_net = m·a) to calculate the net force applied.

2) Work-Kinetic Energy Theorem

In this approach, you calculate the change in the kinetic energy of the bullet, which ends up being the final kinetic energy, as the bullet started from rest (no velocity = no kinetic energy). Using the theorem, you equate the amount of kinetic energy acquired to the amount of work done by the accelerant (assuming that is constant along the whole length. Using the equations (ΔK = W and W = F_net·d) should give you the net force acting on the bullet.

As always, make sure to check the units being used in the quantities provided in the problem. The two methods should give you the same result.