Question

A force $F=-6x^3$ is acting on a block moving along x-axis. Work done by this force is:

• A. Positive in displacing the block from $x=3$ to $x=1$.
• B. Positive in displacing the block from $x=-3$ to $x=-1$.
• C. Negative in displacing the block from $x=0$ to $x=4$.
• D. Zero in displacing the block from $x=-2$ to $x=+2$.

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A Zero in displacing the block from $x=-2$ to $x=+2$.
B Positive in displacing the block from $x=3$ to $x=1$.
C Positive in displacing the block from $x=-3$ to $x=-1$.
D Negative in displacing the block from $x=0$ to $x=4$.

For $\left(A\right):$ Displacement $<0$ and $F<0$ so $W>0$

For $\left(B\right):$ Displacement $>0$ and $F>0$ so $W>0$

For $\left(C\right):$ Displacement $>0$ and $F<0$ so $W<0$

For $\left(D\right):$ $W={\int }_{-2}^2-6x^{3}dx=(-\frac{6}{4}){\left(x^4\right)}_{-2}^2=0$