Calculating Speed on an Incline Using the Law of Conservation of Energy

AI Thread Summary
To calculate the skier's speed at the base of a 22-degree incline, it's essential to apply the Law of Conservation of Energy while accounting for friction. The potential energy (PE) at the top converts to kinetic energy (KE) at the bottom, but frictional forces reduce the total mechanical energy available. The work done by friction can be calculated using the coefficient of friction and the normal force, which is derived from the incline angle. Although mass is not provided, it will cancel out in the equations, simplifying the calculations. Understanding how to incorporate friction into the energy balance is crucial for finding the correct speed.
rob stevenson
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Homework Statement


A ski starts from rest and slides down a 22 o incline 75m long. Coefficient of friction is 0.090. What is the skiers speed at the base of the inlcline? Use energy methods

Homework Equations


PE=mgh
KE=mv2/2
W=Fd

The Attempt at a Solution


Since mass was not given I did PE=KE and solved for v. I solved for height with 75sin22. then moved the equation to solve for velocity. The answer i got was not correct.
 
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Mechanical energy is being 'lost' to frictional forces. You need to account for that. I'm sure your book or other resource covers work done by friction. Have a look at that first and if you have a question about how to apply the idea please ask
 
rob stevenson said:
did PE=KE
What about the friction?
 
haruspex said:
What about the friction?
friction force wasn't given and mass wasn't given so I am not fully sure how to incorporate Ff into it.
 
brainpushups said:
Mechanical energy is being 'lost' to frictional forces. You need to account for that. I'm sure your book or other resource covers work done by friction. Have a look at that first and if you have a question about how to apply the idea please ask

yeah i have no clue how to incorporate it that's where the main problem lies...
 
rob stevenson said:
yeah i have no clue how to incorporate it that's where the main problem lies...

Do you have a textbook? There are usually worked examples of these types of problems in introductory books. The work done by friction is usually modeled as the product of the force of kinetic friction and the distance traveled by the object. The force of kinetic friction is the product of the coefficient of kinetic friction and the normal force. You can use the information given in the question to determine the work done by friction. The kinetic energy must be reduced by that amount. Again, looking in your resource for an explanation and example is the first place you should start.

Although you do not know the mass you will find that you won't need it as it will algebraically cancel in your equation which you will see once you have it set up. Give it a shot!
 
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