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

[rob stevenson]

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.

 

[brainpushups]

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

 

[haruspex]

did PE=KE

What about the friction?

 

[rob stevenson]

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.

 

[rob stevenson]

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...

 

[brainpushups]

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!