Question

A 7.5 kg cannon ball leaves a canon with a speed of 185 m/s. Find the average net force applied to the ball if the cannon muzzle is 3.6 m long.

Answer 1

`F=35651.04N`

Step-by-step explanation:

Let's start writing all the data from the question.

We have the mass ''m'' of the cannonball :

`m=7.5kg`

We have the final speed ''Vf'' of the cannonball :

`Vf=185(m)/(s)`

And we have '' Δx '' which is the total distance that the cannonball travelled inside the cannon muzzle :

Δx =
`3.6m`

If we want to find the average net force applied to the ball, we need to find the acceleration of the cannonball (because we already have the mass of the cannonball).

We can use the following equation in order to find the acceleration :

`Vf^(2)=Vi^(2)+2.a`.Δx (I)

Where ''Vi'' is the initial speed.

Where ''a'' is the acceleration

If we replace all the data in the equation (I) (And assuming
`Vi=0` because that is the initial speed of the cannonball before the cannon is shot) :

`(185(m)/(s))^(2)=0^(2)+2.a.(3.6m)`

`a=(34225(m^(2))/(s^(2)))/((2).(3.6m))=4753.47(m)/(s^(2))`

`a=4753.47(m)/(s^(2))`

Now, we can use the Newton's second law of motion to find the force ''F''

`F=m.a`

`F=(7.5kg).(4753.47(m)/(s^(2)))`

`F=35651.04N`

Where ''N'' is the unit Newton a force unit.

We find that the average net force applied to the ball is
`F=35651.04N`