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Fundamentals Of Physics
Found in: Page 172

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Short Answer

In Fig.7 - 30, a block of ice slides down a frictionless ramp at angle θ=50while an ice worker pulls on the block (via a rope) with a force Fthat has a magnitude of 50 N and is directed up the ramp. As the block slides through distance d=0.50 malong 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 J ifthe rope had not been attached to the block.

See the step by step solution

Step by Step Solution

Step 1: Given data

  1. The angle of the ramp from the ground is, θ=$50.
  2. Applied force by rope, Fr=50 N.
  3. Sliding distance, d=0.50 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 doneW = 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=Frd

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

W=-50×0.50W=-25 J

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 Jas comparedto when a rope is attached to the system.

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