Question

A variable force of magnitude F(x) moves a body of mass m along the x-axis from x1 to x2. The net work done by the force in moving the body from x1 to x2 is where v1 and v2 are the body's velocities at x1 and x2. Knowing that the work done by the force equals the change in the body's kinetic energy, solve the problem.

Answer 1

`w=(1)/(2)m(v^2_2-v^2_1)`

Explanation:

We are given that a variable force of magnitude F(x) moves a body along the x- axis from
`x_1` to
`x_2`.

The net work done by the force in moving the body from
`x_1` to
`x_2` .

`v_1`=Velocity of the body at
`x_1`

`v_2=`Velocity of the body at
`x_2`

We know that

Work done=Final kinetic energy-Initial kinetic energy

`w=(1)/(2)mv^2_2-(1)/(2)mv^2_1`

K.E=
`(1)/(2)mv^2`

`Net\;work \;done=(1)/(2)m(v^2_2-v^2_1)`

Hence, the net work done by the force is given by

`w=(1)/(2)m(v^2_2-v^2_1)`