Find speed with friction force and no mass?

[NewDaddyJones]

Find speed with friction force and no mass??

Homework Statement

A ski starts from rest and slides down a 22 degree incline 75m 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? Use energy methods.

Homework Equations

Delta U = Delta K
mgh = (1/2)mv²
Wext = Delta K + FK * d * sin(theta)
Delta K = FK * d * sin (theta)

The Attempt at a Solution

I am stuck, I've tried so many manipulations of formulas that just wouldn't work because I was not provided with a mass. I tried determining what the mass was but I simply couldn't. I tried finding mass from mgh=(1/2)mv² but that doesn't work out, and v does not simply = sqrt.(2gh) because of the friction.

How can I figure out the force of friction without mass, if it's possible? Or should I be asking how do I figure out the mass?

 

[ehild]

How do you calculate the force of friction?

ehild

 

[NewDaddyJones]

FK = MuK * F_N
FK = MuK * mass * acceleration

I know you could cancel the masses out and find the acceleration, etc. but that doesn't help me out here, I've tried it about 2-3 times.

 

[Beer-monster]

Okay not sure if noticed this but if you draw out a force diagram of your system you should find that the normal force is equal to a trigonometric component of the weight. Therefore, you can calculate the force from the weight and the angle and watch the masses cancel. Once that's done you can work out the energy the ski loses to friction (i.e. the work done by friction) as you know how long your slope is.

Hope that helps.

 

[ehild]

FK = MuK * F_N
FK = MuK * mass * acceleration

F_N is the normal force. Does the skier move normal to the slope? So what is the acceleration in your formula FK = MuK * mass * acceleration ?

ehild

 

[Beer-monster]

The skier does not move normal to the slope.

The force pulling the skier down the slope is gravity. If you split the gravitational force into two components you should find these components equal to the friction and the normal force (because of Newton's 3rd Law). Therefore the acceleration of the normal force is equal to one component of the gravitational acceleration g.

Does that make sense?

 

[NewDaddyJones]

Okay, I understand your concept, however I don't understand how that can eventually give me the final velocity or friction force for that matter.

I applied that concept:

F_N = mg * cos(theta)
mg * cos(theta) = ma ... masses cancel out
g * cos (theta) = a

But dealing with coefficient of friction, so:
g (sin (theta) - MuK * cos (theta) = a

^Using that formula, my a = 2.85 m/s², however, I can't figure out my velocity from here.

 

[Paulie323]

okk well now that you have your acceleration just solve for velocity using the simple kinematics equations using what you know

 

[NewDaddyJones]

Wow, yes - I can't believe I overlooked that, I had the acceleration the whole time, however I was looking at all the equations involving time, overlooking the formula: V² = V_o² + 2a (X-X_o)

Thank you, answer is Vf = 21 m/s