A skier going up a hill

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In summary, the conversation discusses the calculation of work done by kinetic frictional force on a skier coasting up a snow-covered hill. The skier's initial speed and position on the slope are given, as well as their final speed after coasting a certain distance. The attempt at a solution involves finding the change in potential energy and kinetic energy, and using these values to calculate the work done by the frictional force. The final answer is found to be incorrect and the error is identified and corrected.
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omc1
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Homework Statement

A 61.2kg skier coasts up a snow-covered hill that makes an angle of 25.2o with the horizontal. The initial speed of the skier is 8.34m/s. After coasting a distance of 1.97m up the slope, the speed of the skier is 3.43m/s. Calculate the work done by the kinetic frictional force that acts on the skis

Homework Equations

w= ΔE
ke= 1/2mv^2 pe=mgh

The Attempt at a Solution

h=dsin(theta) so i found mu(k) = -1/2mv^2 (final)+1/2mv^2(initial)-mgdsin(theta) all divided by Nd where N=mgcos(theata)

i got 0.654 J...not working?
 
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  • #2
Okay, going a distance d up the slope, at angle \theta, the skier has gone vertically dsin(theta) meters and his potential energy has increased by mgd sin(theta) Joules. The skier's original kinetic energy was (1/2)mv^2(initial) so that increase in potential energy causes a decrease in kinetic energy to (1/2)mv^2(initial)- mgd sin(theta). Since the final kinetic energy is, in fact, (1/2)mv^2(final), they must be an additional loss of energy of (1/2)mv^2(initial)- mgdsin(theta)- (1/2)mv^2(final). That is the "work done by the kinetic frictional force"

The problem does NOT ask for the force itself or the coefficient of friction, which is what you are calculating.
 
  • #3
i got 699.31 J which isn't right, what am i missing i used (1/2)mv^2(initial)- mgdsin(theta)- (1/2)mv^2(final)...
 
  • #4
i found my problem thanks
 
  • #5


I would like to clarify that the given information does not provide enough data to accurately calculate the work done by the kinetic frictional force. The equation you provided, w=ΔE, is correct for calculating work, but it requires the change in energy (ΔE) to be known. In this case, the change in energy would be the difference between the initial kinetic energy and the final kinetic energy, which is not provided in the given information.

To accurately calculate the work done by the kinetic frictional force, we would need to know the coefficient of kinetic friction (μk) between the skis and the snow, as well as the distance traveled by the skier. Without this information, it is not possible to accurately determine the work done by the kinetic frictional force.

Additionally, the equation you used, pe=mgh, is for calculating potential energy, not work. The correct equation for work would be W=Fd, where F is the force applied and d is the distance traveled. However, without knowing the force applied by the kinetic frictional force, we cannot accurately calculate the work.

In conclusion, without the necessary information, it is not possible to accurately calculate the work done by the kinetic frictional force on the skier going up the hill. More data, such as the coefficient of kinetic friction and the distance traveled, would be needed to accurately determine the work done.
 

What is the physics behind a skier going up a hill?

When a skier is going up a hill, they are essentially overcoming the force of gravity. The skier's muscles provide the necessary force to propel them up the hill. In addition, the skis' edges create a friction force against the snow, allowing the skier to gain traction and move forward.

Why do skiers lean forward when going up a hill?

Skiers lean forward when going up a hill to maintain their balance and prevent themselves from falling backwards. This also allows them to put more weight on their skis, increasing their friction force against the snow and helping them move up the hill more efficiently.

How does the angle of the hill affect a skier going up?

The angle of the hill plays a significant role in a skier's ability to go up the hill. The steeper the hill, the more force the skier will have to exert to overcome gravity. Additionally, a steeper hill can also increase the speed at which the skier goes down the hill, requiring them to use more control and technique.

What techniques do skiers use to go up a hill?

Skiers use a variety of techniques to go up a hill, including the herringbone technique, where they angle their skis outwards to create a "V" shape and push off the inside edges of their skis. They may also use a sidestep technique, where they move up the hill by stepping one ski at a time in a sideways motion. In some cases, skiers may also use ski lift or rope tow systems to assist them in going up the hill.

How does the weight of the skier affect their ability to go up a hill?

The weight of the skier can significantly impact their ability to go up a hill. Generally, a heavier skier will have an easier time going up a hill, as they will have more force to push against gravity. However, a skier's technique and skill also play a significant role in their ability to go up a hill, regardless of their weight.

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