Question

A man pushes a $15\text{kg}$ box of books $2.0\text{m}$ up a ${37}^{\circ }$ incline into the back of a moving van. The box moves at a constant velocity if you push it with a force of $95\text{N}$. Find the work done by gravity on the box. Take $(g=10{\text{m/s}}^2)$

• A. $-180\text{J}$
• B. $-120\text{J}$
• C. $180\text{J}$
• D. Zero

Answer 1

The correct option is A $-180\text{J}$

$FBD$ of system is

From $FBD$ of the block, we have the component of weight down the incline plane as $mg\sin \theta$ and the displacment is up the incline plane $d=2.0\text{m}$, the other component of weight will be perpendicular to plane $mg\cos \theta$.

Now here the work done will be due to the force component along the plane only which is, $F=mg\sin \theta$.
The angle between $F$ and $d$ is ${180}^{\text{o}}$

Hence work done by gravity will be only due to the force along the incline plane $W_g=\overrightarrow{F}.\overrightarrow{s}=\left(mg\sin {37}^{\text{o}}\right)\times 2\times \cos {180}^{\text{o}}$

$W_g=-180\text{J}$

Hence option A is the correct answer