Question

After the box comes to rest at position x1, a person starts pushing the box, giving it a speed v1. when the box reaches position x2 (where x2>x1), how much work wp has the person done on the box? assume that the box reaches x2 after the person has accelerated it from rest to speed v1. express the work in terms of m, v0, x1, x2, and v1.

Answer 1

As we know by work energy theorem

total work done = change in kinetic energy

so here we can say that wok done on the box will be equal to the change in kinetic energy of the system

$W_p = KE_f - KE_i$

initial the box is at rest at position x = x1

so initial kinetic energy will be ZERO

at final position x = x2 final kinetic energy is given as

$KE_f = \frac{1}{2}mv_1^2$

now work done is given as

$W_p = \frac{1}{2}mv_1^2 - 0$

so we can say

$W_p = \frac{1}{2}mv_1^2$

so above is the work done on the box to slide it from x1 to x2