Question

A bullet of mass 20 gram going with a velocity of 500 m per second strikes a tree and goes out from other side with the velocity 400 m per second calculate the work done by the bullet passing the tree

Answer 1

As work = Force * displacement

 Or W = F * s

It can be also written as W = m * a * s

Now, velocity of bullet before hitting the tree is u and is 500 m s-1 and after hitting the tree is v and is 400 m s-1

Apply the 3rd equation of motion , v 2 = u 2 + 2 a s

here , velocity decreases so body retards and equation also changes as v 2 = u 2 - 2 a s

put u = 500 m s-1  and v = 400 m s-1

=> ( 400 )2 = ( 500 )2  - 2 a s

=> 2 a s = ( 500 )2 - ( 400 )2

=> 2 a s = ( 500 - 400 )( 500 + 400 )  { from the identity in maths a 2 - b2 = ( a + b )(a - b ) }

=> 2 a s = 100 * 900

=>  a s = 45000 ,let this equation be named as ( 1 ) Or  a s = 45000 ............. ( 1 ) 

Now W = m * a * s

as m and a * s are given 

put these given values in the above given equation

 So W = ( 20 / 1000 ) { as work is measured in J ,so for Joules mass is considered in kgs } * 45000

=> W = 20 * 45

=. W = 900 J

So ,work done by the bullet is 0.9 kJ or 900 J