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here is the question word for word along with answer choices. Keep in mind i already know the answer is letter b i just need to know how i get there.

An Olympic skier moving at 20m/s down a 30.0 degree slope encounters a region of wet snow and slides 145m before coming to a halt. What is the coefficient of friction between the skis and the snow?

a. 0.540 c. 0.116
b. 0.740 d. 0.470

So far with this problem i have found delta T and acceleration but i'm stuck.

2006-11-04 11:13:07 · 2 answers · asked by strawberrylollipop12345 1 in Science & Mathematics Physics

2 answers

I was able to get u = 0.74, here's how i did it:

First, draw a free-body diagram to show the forces acting on the skier. In this problem, we have 3, the weight of the skier, the normal force on the skier, and the frictional force.

To set up your axes, it would be simpler to make the axes coinicide with the Normal and Frictional forces (since they are perpendicular). We can deduce Newton's 2nd law easily since the motion of the skier is the parallel opposite of the frictional force. Now set-up Netwon's 2nd law equations in x and y. We only have to break up the weight using trig into components parallel to the frictional and normal forces. Also, let's denote F as the frictional force

'y' direction ----------> N - mgcos(theta) = 0 [because the skier is not moving in this direction]

'x' direction ---------> mgsin(theta) - F = ma

Using these two equations, we know that N = mgcos(theta) and F = uN

Simplifying, you get F = u*m*g*cos(theta). Thus, the 2nd equation simplifies to:

m*g*sin(theta) - u*m*g*cos(theta) = m*a

The masses cancel, now isolate u:

u = [g*sin(theta) - a]/[g*cos(theta)]

Now all we need is to find 'a' and we can solve for 'u'. We need to use constant acceleration equation to solve for 'a'. Since the motion is all parallel to the frictional force, this can be done.

I used ----------> 2ax = v_f^2 - v_i^2

Using x = 145m, v_f = 0, and v_i = 20, solve for a:

a = (v_f^2 - v_i^2)/(2x) = -400/(2*145). Therefore, a = -1.38 m/s^2. In this case, direction does matter (don't forget the negative)

Plugging this negative value for a, the numerator of u becomes positive. Thus now you can solve for 'u':

u = (9.8*sin(30) + 1.38)/(9.8*cos(30))

Solving, I got u = 0.74

-------------

Hope this helps

2006-11-04 13:33:40 · answer #1 · answered by JSAM 5 · 0 0

Well, I've tried this over and over. I'm a bit rusty but I'm pretty sure your answers there are all wrong. I got something like 0.659 which might be a few thousandths out depending on what you took g as and rounding.

I'll tell you how to do it anyway.

First resolve perpendicular to slope. This gives you normal reaction (R) = mg cos 30 = ( (root 3)/2 ) * mg

Now apply Newton 2 parallel to the slope. Don't forget that the resultant force slowing down the skiier is friction less the component of gravity down the slope. The mass cancels leaving you with ( (root 3)μ - 1) g = a
where a is your accelleration and μ is coeff. of friction.

Now put that into the constant accelleration formula v squared = u squared + 2as (where v is final speed of 0, u is 20 and s is distance) and you get a = -200/145 = 1.379 m / (s squared.)

You can ignore the minus (it just tells you that the accelleration is such that it's slowing the skiier). You've taken account of that by resolving parallel to the slope before.

Now if you sub in the value for a into the slope equation ( (root 3)μ - 1) g = a then you get
( (root 3)μ - 1) g = 1.379
( (root 3)μ - 1) = 0.1406
(root 3)μ = 1.1406
μ = 0.659

If you can see where I went wrong then I'd love to know. I'd suggest doing your best with it then seeing your tutor. Often by trying really hard on a question and getting stuck, you'll understand it better when the tutor explains it.

==================================
Edit:
JSAM's solution is correct. I made the classic mistake of putting in numbers too early. I should do these more often, get back into it. A good answer JSAM, thorough and neatly explained.

2006-11-04 12:51:44 · answer #2 · answered by Aranta 2 · 0 1

Diagram the forces on the block. Split gravity into components along the incline and perpendicular to it. Balance the forces to write an expression for the total force in terms of the coefficient of kinetic friction. Put that into the equation F = ma. Solve for μ.

2016-03-19 03:34:53 · answer #3 · answered by Anonymous · 0 0

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