Question

A 4.79 g bullet moving at 642.3 m/s penetrates a tree trunk to a depth of 4.35 cm. Use work and energy considerations to find the magnitude of the force that stops the bullet. Answer in units of N.

Answer 1

Force,
`F=2.27* 10^4\ N`

Step-by-step explanation:

Given that,

Mass of the bullet, m = 4.79 g = 0.00479 kg

Initial speed of the bullet, u = 642.3 m/s

Distance, d = 4.35 cm = 0.0435 m

To find,

The magnitude of force required to stop the bullet.

Solution,

The work energy theorem states that the work done is equal to the change in its kinetic energy. Its expression is given by :

`F.d=(1)/(2)m(v^2-u^2)`

Finally, it stops, v = 0

`F.d=-(1)/(2)m(u^2)`

`F=(-mu^2)/(2d)`

`F=(-0.00479* (642.3)^2)/(2* 0.0435)`

F = -22713.92 N

`F=2.27* 10^4\ N`

So, the magnitude of the force that stops the bullet is
`2.27* 10^4\ N`