Question

A block of mass $1\text{kg}$ slides down on an inclined plane of inclination ${30}^{\circ }$. Find the work done by the block's weight as it slides through $50\text{cm}$.

• A. $4.45\text{J}$
• B. $3.45\text{J}$
• C. $1.45\text{J}$
• D. $2.45\text{J}$

Answer 1

The correct option is D $2.45\text{J}$


Suppose the block slides from A to B.
The displacement is $AB=50\text{cm}=0.5\text{m}$ along the inclined plane. The weight is
$mg=\left(1\text{kg}\right)\times \left(9.8{\text{m/s}}^2\right)=9.8\text{N}$ in the downward direction.

The angle between the force and the displacement is ${60}^{\circ }$ as shown in the figure.
Hence, the work done by the weight is
$W=\left(9.8\text{N}\right)\times \left(0.50\text{m}\right)\times \left(\cos {60}^{\circ }\right)$
$\therefore W=\left(9.8\text{N}\right)\times \left(0.50\text{m}\right)\times \frac{1}{2}=2.45\text{J}$