91Ó°ÊÓ

1. The angle of the ramp from the ground is, $\mathrm{θ}=\${50}^{∘}$.
2. Applied force by rope, $F_{\text{r}}=50\text{N}$.
3. Sliding distance, $d=0.50\text{m}$.

From the figure, we can say thattheblock is moving inadownward direction. If the rope is attached, the kinetic energy will decrease by some amount. We have to find this kinetic energy.

Formula:

Work done$W=Fd$

We know thatthework done can be calculated as,

$W=F_{r}d$

Substitute the values in the above expression, and we get,

$$\begin{gathered} W=-\left(50×0.50\right) \\ W=-25\text{J} \end{gathered}$$

The negative sign says thatthe work done is alongthe opposite direction of motion ofthe block, which means the motion of the block and the pull from the rope are in opposite directions.

If there is no rope attached to the system,the block will move freely downward. Hence, kinetic energy will increase by $25\text{J}$as comparedto when a rope is attached to the system.