Question

A child applies a force $F$ parallel to the $x$-axis to a block moving on a horizontal surface. The $x$-component of the force varies with the $x$-coordinate of the block as shown in figure. The work done by the force $F$ when the block moves from $x=0$ to $x=7\text{m}$ and $x=3\text{m}$ to $4\text{m}$ are (in joules)

• A. $-3,0$
• B. $0,0$
• C. $3,0$
• D. $-3,3$

Answer 1

The correct option is C $3,0$

Work done $\left(W\right)=$ Area under $F-x$ graph
When the block moves from $x=0$ to $x=7m$:
$W=$ Area of $△AEO+$ Area of rectangle $ABFE-$ Area of $△POQ$
$=\frac{1}{2}\times (2-0)\times 2+(3-2)\times 2-\frac{1}{2}\times (6-4)\times 1=2+2-1=3\text{J}$
From $x=3\text{m}$ to $x=4\text{m}$, Applied force = $0$
$\therefore$ Work done = $0\text{J}$