Solve Work Energy Problem: Find Theta for Skier on Slope

In summary, a skier with an initial speed of 1.9m/s slides down a 10.2m long slope inclined at an unknown angle (theta) to the horizontal. The coefficient of kinetic friction is 0.11 and air resistance is negligible. The skier's final speed at the bottom of the slope is 8.3m/s. Using the equations F=ma and Work(friction) = (delta)Kinetic Energy + (delta) Potential Energy, we can find that these two are mathematically equivalent and cancel each other out when substituted. To find (theta), we can either find the height of the hill or the horizontal distance traveled.
  • #1
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A skier slides down a slope 10.2m long, inclined at an angle (theta) to the horizontal. The coefficient of kinetic friction is 0.11. Skier's initial speed is 1.9m/s and final speed at the bottom of the slope is 8.3m/s. Find (theta), air resistance is negligible.

I have applied F=ma and Work(friction) = (delta)Kinetic Energy + (delta) Potential Energy to it and found that these two r mathematically equivallent and terms just cancel when i substitue, can any1 help me with this one?

Thx
 
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  • #2
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A skier slides down a slope 10.2m long, inclined at an angle (theta) to the horizontal. The coefficient of kinetic friction is 0.11. Skier's initial speed is 1.9m/s and final speed at the bottom of the slope is 8.3m/s. Find (theta), air resistance is negligible.

I have applied F=ma and Work(friction) = (delta)Kinetic Energy + (delta) Potential Energy to it and found that these two r mathematically equivallent and terms just cancel when i substitue, can any1 help me with this one?

Thx

try finding the height of the hill. you should then be able to solve for theta.

if you can find the Horizontal distance traveled, that would also be acceptable.
 
  • #3
How can i find the height with only one side of the triangle known? Where solving it would involve the angle itself?
 

1. How do I calculate the work done by a skier on a slope?

The work done by a skier on a slope can be calculated using the formula W = Fdcosθ, where W is the work done, F is the force applied, d is the displacement of the skier, and θ is the angle between the force and the displacement.

2. What is the relationship between work and energy in this problem?

In this problem, work and energy are directly related. The work done by the skier is equal to the change in the skier's kinetic energy. This means that when the skier is moving, the work done is positive, and when the skier is at rest, the work done is zero.

3. How can I find the angle θ for a skier on a slope?

To find the angle θ, you will need to know the force applied by the skier, the displacement of the skier, and the work done by the skier. Then, you can rearrange the formula W = Fdcosθ to solve for θ.

4. Can I use this formula for any slope angle?

Yes, this formula can be used for any slope angle. However, keep in mind that the angle used in the formula is the angle between the force applied and the displacement, not the angle of the slope itself.

5. How does the mass of the skier affect the solution to this problem?

The mass of the skier does not affect the solution to this problem. The formula for finding θ takes into account the force applied by the skier, which is dependent on the skier's weight. Therefore, the mass of the skier is already factored into the formula.

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