# A machine gun fires bullets at a rate of 600 per minute. If each bullet has a mass of 60g and a muzzle velocity of 400m/s, what is the force that the gunner must apply, in order to stop it from moving back?

Jan 20, 2017

The gunner must apply $240 N$ to the gun to stop it from moving back.

#### Explanation:

Newton's third law states that the force applied by an object to another object is equal to the force applied by the second object on the first. Thus, the bullet exerts the same force on the gun as the gun applies to the bullet.

First, we need to find the acceleration of the bullet. For this we use
$a = \frac{\Delta v}{\Delta t}$
In this case
$\Delta v = 400 \frac{m}{s}$ because the initial velocity is 0 and $\Delta t = \frac{60 s}{600} = \frac{1}{10} s$

Using these two values we can get the acceleration

$a = \frac{400 \frac{m}{s}}{\frac{1}{10} s} = 10 \cdot 400 \frac{m}{s} ^ 2 = 4000 \frac{m}{s} ^ 2$

Now we'll use Newton's second law to find the force needed to accelerate the bullet. Newton's second law says that force is a product of mass and acceleration.
$F = m a = 0.06 k g \cdot 4000 \frac{m}{s} ^ 2 = 240 k g \frac{m}{s} ^ 2 = 240 N$