Q12DQ - University Physics with Modern Physics

Question

Can the total work done on an object during a displacement be negative? Explain. If the total work is negative, can its magnitude be larger than the initial kinetic energy of the object? Explain.

Step-by-Step Solution

Answer

The total work done on an object can be negative, and the magnitude of work cannot be larger than the initial kinetic energy. 

Step 1: Describe the Work-Energy theorem

The work energy theorem tells that the work done on the body results in a change in its kinetic energy.

$$\begin{gathered} {\mathit{W}}_{\mathbf{t}\mathbf{o}\mathbf{t}\mathbf{a}\mathbf{l}}\mathbf{=}{\mathit{K}}_{\mathbf{2}}\mathbf{-}{\mathit{K}}_{\mathbf{1}} \\ \mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{ }\mathbf{=}\mathbf{∆}\mathit{K} \end{gathered}$$

Step 2: Determine whether total work done on an object during a displacement be negative and if negative then find whether its magnitude be larger than the initial kinetic energy of the object

From the work-energy theorem, the total work done on an object during a displacement can be negative if  $K_1>K_2$.

 

If the total work is negative, then

$$\begin{gathered} W_{tot}=K_2-K_1<0 \\ =K_1-K_2>0 \\ {W}_{tot}+K_2=K_1>0 \end{gathered}$$

From this relation, it is concluded that the magnitude of work cannot be larger than the initial kinetic energy.