Energy - Ski sliding down a ramp

[Ritzycat]

Homework Statement

A ski starts from rest and slides down a 28^∘ incline 65m long. If the coefficient of friction is 0.090, what is the ski's speed at the base of the incline? If the snow is level at the foot of the incline and has the same coefficient of friction, how far will the ski travel along the level?

Homework Equations

KE = (1/2)mv²
PE_g = mgh

Note that I want to solve this problem using energy relations, not kinematics.

The Attempt at a Solution

Taking Point A to be the top of the ramp, point B to be right before the bottom.

PE_g = KE + E_diss
mgh = (1/2)mv² + F_f
mgh = (1/2)mv² + μF_N
mgh = (1/2)mv² + μmg(sin 30^∘)
gh = (1/2)v² + μg(sin 30^∘)
(9.8m/s²)(30.5157m) = (1/2)(v²) + (0.090)(9.8m/s²)(sin 30^∘)

v = 24.4 m/s.

That answer was incorrect. I have not yet attempted the second question since I don't have a correct answer for the first one.

 

[Tanya Sharma]

The Attempt at a Solution

Taking Point A to be the top of the ramp, point B to be right before the bottom.

PE_g = KE + E_diss
mgh = (1/2)mv² + F_f
mgh = (1/2)mv² + μF_N
mgh = (1/2)mv² + μmg(sin 30^∘)
gh = (1/2)v² + μg(sin 30^∘)
(9.8m/s²)(30.5157m) = (1/2)(v²) + (0.090)(9.8m/s²)(sin 30^∘)

v = 24.4 m/s.

That answer was incorrect. I have not yet attempted the second question since I don't have a correct answer for the first one.

First thing, The angle of incline is 28^∘ ,not 30^∘. Secondly work done by friction is not μN.

 

[ehild]

The Attempt at a Solution

Taking Point A to be the top of the ramp, point B to be right before the bottom.

PE_g = KE + E_diss
mgh = (1/2)mv² + F_f

The dissipated energy is not equal to the force of friction.

 

[Ritzycat]

First , The angle of incline is 28^∘ ,not 30^∘. Secondly work done by friction is not μF_N.

Thanks for the reminder - although when I plugged in the new value, the answer changed very minimally...

The dissipated energy is not equal to the force of friction.

What should I set E diss equal to then??

 

[Tanya Sharma]

Energy dissipated is equal to the work done by friction . How do you calculate the work done by a force ?

 

[ehild]

Thanks for the reminder - although when I plugged in the new value, the answer changed very minimally...
What should I set E diss equal to then??

Do you think that energy is the same as force?

 

[Ritzycat]

Energy dissipated is equal to the work done by friction . How do you calculate the work done by a force ?

F_f * d = W

I think that will yield me the right answer. I would use the length of the incline, since that is the direction Friction was acting in. Then I'll plug it in. I'm right about to go to bed, so I'll do that in the morning.

Do you think that energy is the same as force?

No I forgot to multiply it by Distance....! i get it now Silly Ritzycat

 

[ehild]

Such things do happen :)