Question

a force exerts an impulse J on a body by changing its speed U to V.Force and objects are along the same line.Show that work done by the force is J(U+V)/2.

Answer 1

According to the relation [J=∆P] where J= impulse and ∆P is change in linear momentum, we can get mass of the object as:
J=m(V-U). ( m= mass of object)
=> m=J/(V-U)...........(1)
further,
according to work energy theorem:
W(work done)= change in KE .

W=(1/2)×m×(V^2-U^2).........(2)

putting value of m from (1) in (2) and solving we get the desired result.

Answer 2

We know that

J = ∆ P (∆P is change in linear

momentum)

J = m(V-U)

m = J/(V-U)..................(1)

According to the work energy theorem

W = ∆ K.E.

W= 1/2 m (V^2-U^2)

Putting value of m from eq. 1

W= J/2 (V-U) or

W= J (U+V)/2

By Sonam Tyagi