Question

How do you find the force needed to accelerate a 0.007 kg pellet from rest to 125 m/s over a distance of 0.8 m along the barrel?

Answer 1

The force is `=68.36N`

Explanation:

Apply the equation of motion

`v^2=u^2+2as`

The initial velocity is `u=0ms^-1`

The final velocity is `v=125ms^-1`

The distance is `s=0.8m`

The acceleration is

`a=(v^2-u^2)/(2s)=(125^2)/(2*0.8)=9765.625ms^-2`

The mass of the pellet is `=0.007kg`

According to Newton's Second Law of Motion

`F=ma`

The force is `F=0.007*9765.625=68.36N`

Answer 2

`F= 68.36 N`

Explanation:

`m=0.007` `Kg`
`u=0` `ms^-1`
`v=125` `ms^-1`
`s=0.8 m`

Applying a motion equation:

`v^2=u^2 + 2as`
`15 625 = 1.6a`
`a= 9765.625` `ms^-2`

Applying Newton's second law:

`F = ma`
`F=0.007 * 9765.625`
`F= 68.36 N`

Again, that's valid assuming we have no other forces on the motion axis acted on the object whatsoever.