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Found in: Page 172

### Fundamentals Of Physics

Book edition 10th Edition
Author(s) David Halliday
Pages 1328 pages
ISBN 9781118230718

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# In Fig.${\mathbf{7}}{\mathbf{}}{\mathbf{-}}{\mathbf{}}{\mathbf{30}}$, a block of ice slides down a frictionless ramp at angle ${\mathbit{\theta }}{\mathbf{=}}{{\mathbf{50}}}^{{\mathbf{\circ }}}$while an ice worker pulls on the block (via a rope) with a force $\stackrel{\mathbf{\to }}{\mathbf{F}}$that has a magnitude of ${\mathbf{50}}{\mathbf{}}{\mathbf{}}{\mathbit{N}}{\mathbf{}}$and is directed up the ramp. As the block slides through distance ${\mathbit{d}}{\mathbf{=}}{\mathbf{0}}{\mathbf{.}}{\mathbf{50}}{\mathbf{}}{\mathbit{m}}$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?

Kinetic Energywould begreater by $25\text{J}$ ifthe rope had not been attached to the block.

See the step by step solution

## Step 1: Given data

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, $d=0.50\text{m}$.

## Step 2: Understanding the concept

From the figure, we can say thatthe block 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$W=Fd$

## Step 3: Calculate how much greater would the kinetic energy have been if the rope had not been attached to the block

We know that the work done can be calculated as,

$W={F}_{r}d$

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

$W=-\left(50×0.50\right)\phantom{\rule{0ex}{0ex}}W=-25\text{J}\phantom{\rule{0ex}{0ex}}$

The negative sign says thatthe work done is along the opposite direction of motion of the 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.

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