Friction and acceleration problem

[Havenater23]

Homework Statement

A 50 kg skier skies down a 25 degree slope, calculate the acceleration.

Homework Equations

The Attempt at a Solution

It seems pretty simple, I can get all the way down to the Net force of X and get something like : Fx = Sin(25)mg - Cos(25)mgU = ma.

Which I get something like 4.73 m/s^2 .
Can someone else help me get the right answer? I don't know if this one is correct.

 

[Sourabh N]

The skier is accelerating because of gravity. Had there been no slope, he'd simply fall down with acceleration g. Since there is slope, only a component of gravity (along the slope) is effective. What is the component of gravity along the slope?

 

[Havenater23]

I understand that gravity is causing the acceleration. But there should be still something different. Gravity's acceleration is 9.8 m/s^2.

 

[Sourabh N]

The something different is that "effectively" only a component of gravity is acting. Are you familiar with free body diagram? Draw one and you will see that the component of gravity perpendicular is canceled by reaction force on the skier by the ramp, thus leaving you only with the component along the ramp.

 

[Havenater23]

Yeah, I know freed body diagrams, and I understand that acceleration of y= 0
But Fn=Cos(25)mg

 

[Sourabh N]

If 25 degree is the slope of ramp with respect to ground, yes, Fn = mgCos(25). The skier is accelerating along the ramp, so ma = mgSin(25).

 

[Havenater23]

Yeah, but isn't there a friction force as well,

 

[Sourabh N]

Since there was no mention of friction in your question, I was assuming there is not friction. Does the problem say anything about friction?

 

[Havenater23]

No, it doesn't mention it. I guess you are right, if it doesn't mention friction then why put it in there. I guess I've just been doing too many problems that have frictions. Ha