# Solving Compression Problem: Water Skier & Tow Rope

• shaka23h
In summary, a 57-kg water skier is being pulled by a nylon tow rope with a Young's modulus of 3.7 x 109 N/m2 and a cross-section area of 1.9 x 10-5 m2. The unstretched length of the rope is 18 m. As the skier moves, a resistive force of 190 N acts on her in the opposite direction, resulting in a net force that causes an acceleration of 0.81 m/s2. Using the equation F = Y(Delta L/L0)A, the change in length of the rope can be calculated to be FL0/ Y(A).
shaka23h
A 57-kg water skier is being pulled by a nylon (Young's modulus 3.7 x 109 N/m2) tow rope that is attached to a boat. The unstretched length of the rope is 18 m and its cross-section area is 1.9 x 10-5 m2. As the skier moves, a resistive force (due to the water) of magnitude 190 N acts on her; this force is directed opposite to her motion. What is the change in length of the rope when the skier has an acceleration whose magnitude is 0.81 m/s2?

Ok here is what I was able to do so far I know that

F = Y(Delta L/L0)A

When I solve for Delta L I know that Delat L = FL0/ Y(A).

I just don't know how to factor in the acceleration and most importantly how to use the 190 N resistence force?

Please let me know and thanks a lot.

The acceleration of the skier is the result of the net force acting. The net force is the combination of the force from the rope and the resistive force.

oh ic ic.

That explains it so much better.

Thank you so much.

## What is the compression problem in water skiing?

The compression problem in water skiing refers to the force exerted on the tow rope by the skier's weight and speed. This force can cause the rope to stretch and lose tension, making it difficult for the skier to maintain their position and balance.

## How does the compression problem affect the water skier?

The compression problem can cause the water skier to experience a jerking or bouncing motion, which can lead to loss of balance and control. It can also make it more difficult for the skier to make sharp turns and perform tricks.

## What are some solutions to the compression problem?

One solution to the compression problem is to use a tow rope with a higher breaking strength and lower stretch, such as a polyethylene or Spectra rope. Another solution is to adjust the length of the rope to reduce the distance between the skier and the boat, which can minimize the effects of compression.

## How does the weight of the water skier affect the compression problem?

The weight of the water skier can significantly impact the compression problem. A heavier skier will exert more force on the tow rope, causing it to stretch and lose tension more quickly. This can be mitigated by using a tow rope with a higher breaking strength or by adjusting the length of the rope.

## Are there any safety concerns associated with the compression problem?

Yes, the compression problem can pose safety concerns for both the water skier and the boat driver. If the tow rope becomes too stretched, it can snap and potentially injure the skier or those nearby. It is important to regularly inspect and replace old or worn tow ropes to prevent accidents.

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