Terminal Speed for Skier Going Down Slope

In summary, an area skier going down a snow-covered slope on wooden skis has a terminal speed of 57 m/s.
  • #1
adamwest
10
1

Homework Statement



What is the terminal speed for an 75.0kg skier going down a 35.0∘ snow-covered slope on wooden skis μk= 0.060?

Assume that the skier is 1.60m tall and 0.300m wide.

Express your answer using two significant figures with the appropriate units.

Area skier = A = (1.60m x 0.300m) = .48 m^2

Homework Equations



D = (1/4)A*v^2
Fnet = D

The Attempt at a Solution



(mgsinθ) - (μk*mgcosθ) = (1/4)A*v^2

=> vterminal = sqrt((4((mgsinθ) - (μk*mgcosθ))) /A )

vterminal = sqrt((4((75.0 * 9.80 * sin(35)) - (.060 * 75.0 * 9.80 * cos(35))))/.48)

vterminal = 56.68 m/s = 57 m/s (rounded to 2 sig figs)

Mastering Physics says that this answer is wrong but I cannot find my error. I have checked over the problem and my solution about a dozen times. I figure more experienced eyes may help find my ruinous mistake. Thank you! :)
 
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  • #2
Your work looks good to me. The data in the problem is given to 3 significant figures. Maybe you are supposed to keep 3 sig figs in the answer. Don't know.
 
  • #3
Thanks for double checking for me, I really appreciate it. :)

I actually tried submitting it with 3 sig figs as well but it said it was wrong. I am going to email my professor and see if they can take a look.
 
  • #4
D = (1/4)A*v^2

I believe this equation for drag force assumes a spherical shape for the drag coefficient (C_drag = about 0.5) . If the skier is standing more or less upright rather tham curled up like a ball, the drag coefficient is higher, and thus the terminal speed will be less. The quadratic drag force is actually 1/2(C_drag)ρ(A)v^2, where ρ is the air density(about 1.2 kg/m^3), and C_drag for a flat exposed surface might be more like 1.0 or so.
When I last went snow tubing, I knew my speed was much faster when lying back instead of sitting up. And faster than that when going with my grandkids 2 or more per tube and faster than that with several tube loads of kids hooked together in a lying down position! What a rush!
 
  • #5
It looks like you were right, PhantomJay. I should have seen this before but I didn't check my units. The answer is as follows:

sqrt((2mg/ACp)*(sinθ-μkcosθ))

If you do it this way then you get all of the correct units (m/s) in the end after taking the square root. I used the following:

p (rho) = 1.2 kg/m^3
m = 75.0 kg
g = 9.80 m/s^2
θ = 35 degrees
μk = 0.060
C = 0.8

When you plug all of these into the equation you get a terminal velocity of v = 41 m/s (to 2 significant figures), which is the correct answer.

The only thing I am still unclear on is why we use a drag co-efficient of C = 0.8, which closely resembles a cylinder falling end-down, instead of a drag co-efficient of C = 1.1, which closely resembles a cyclinder falling side-down. I feel like a skier standing upright is affected by drag more similarly to the side of a cylinder than the bottom of one. Perhaps it has to do with the fact that they are falling at an angle? I don't know.

Anyways, thank you all for your help! :)
 
  • #6
Thank you So much Sir/Madam, i tried a thousand times, spent an hour and 15 mins trying, but failing. Thank you again!
 

What is terminal speed for a skier going down a slope?

Terminal speed, also known as terminal velocity, is the maximum speed that a skier can reach while going down a slope. It is the point at which the force of air resistance equals the force of gravity, resulting in a constant and balanced speed.

How is terminal speed calculated for a skier going down a slope?

The terminal speed for a skier going down a slope can be calculated using the formula: Vt = √(2mg/pAC), where Vt is the terminal speed, m is the mass of the skier, g is the acceleration due to gravity, p is the density of air, A is the frontal area of the skier, and C is the drag coefficient.

What factors affect the terminal speed of a skier going down a slope?

The terminal speed of a skier going down a slope is affected by several factors including the skier's mass, the slope of the slope, the skier's frontal area, the density of the air, and the drag coefficient of the skier's equipment and clothing.

Can a skier exceed their terminal speed while going down a slope?

No, a skier cannot exceed their terminal speed while going down a slope. This is because at terminal velocity, the forces acting on the skier are balanced, resulting in a constant speed. If the skier were to exceed their terminal speed, the force of gravity would be greater than the force of air resistance, causing the skier to accelerate.

How does the slope angle affect the terminal speed of a skier?

The slope angle does not have a direct effect on the terminal speed of a skier. However, a steeper slope will result in a faster acceleration, which in turn will reach the terminal speed faster. A shallower slope will result in a slower acceleration, taking longer for the skier to reach their terminal speed.

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