In Fig.$\mathbf{7}\mathbf{}\mathbf{-}\mathbf{}\mathbf{30}$, a block of ice slides down a frictionless ramp at angle $\mathit{\theta }\mathbf{=}{\mathbf{50}}^{\mathbf{\circ }}$while an ice worker pulls on the block (via a rope) with a force $\overrightarrow{\mathbf{F}}$that has a magnitude of $\mathbf{50}\mathbf{}\mathbf{}\mathit{N}\mathbf{}$and is directed up the ramp. As the block slides through distance $\mathit{d}\mathbf{=}\mathbf{0}\mathbf{.}\mathbf{50}\mathbf{}\mathit{m}$along the ramp, its kinetic energy increases by . How much greater would its kinetic energy have been if the rope had not been attached to the block?

1. The angle of the ramp from the ground is, $\theta =\${50}^{\circ }$.
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,

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

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.