Question

C) A cannon has a mass of 80kg and the ball has a mass of 3kg. The explosion produces a mean force of 400 N that lasts for 0.2 seconds. Calculate the final velocity of the cannon and the ball and prove that the final momentum is zero.?

Answer 1

`1\ m/s` & `26.667\ m/s`

Explanation:

The impulse of the explosive force `400\ N` acting for `0.2`seconds will cause in the momentum of ball & the cannon by the same amount

The explosive force `F=400\ N` will cause change in momentum of cannon of mass `m=80\ kg` in times `t=0.2` sec increasing velocity from rest `u=0` to final velocity `v`

From Newton's second law

`F=\frac{d(mv)}{dt}`

`F=\frac{m(v-u)}{t}`

`400=\frac{80(v-0)}{0.2}`

`80v=80`

`v=1\ m/s`

Now, the explosive force `F=400\ N` will cause change in momentum of ball of mass `m=3\ kg` in times `t=0.2` sec increasing velocity from rest `u=0` to final velocity `v`

From Newton's second law

`F=\frac{d(mv)}{dt}`

`F=\frac{m(v-u)}{t}`

`400=\frac{3(v-0)}{0.2}`

`3v=80`

`v=80/3`

`=26.667\ m/s`

By the law of conservation of linear momentum, the momentum before explosion & after explosion remains will be equal. But before ball & cannon both are at rest i.e. momentum before explosion is zero hence the momentum after explosion will also be zero