Help with interesting problem of impact forces

[a_skier]

Ok so I am a professional freestyle skier who jumps off of cliffs into powder (light fluffy snow). I found a big cliff that I may go jump off and I know that it is physically possible to land and ski away from, but I also have an interest in physics, (with 0 knowledge), and I have been trying to find a way to calculate the impact force upon my legs when I hit the ground.

I don't know if you guys use metric or not so I'm going to use imperial. Let's say that this cliff is 60 feet tall, and I will be skiing off of it at 10 mph. I will not penetrate into the landing anymore than 3 feet. And the landing is at an angle of 40 degrees.



I got something like 2000 lbs. of impact but my problem is that I don't know how to allow for the angle of the slope, and I know that stuff like this has been done HUNDREDS of times, so can someone set me on the right path?

Thanks so much guys!

-Austin

 

[a_skier]

can on one see this? I notice the title of my thread isn't in bold. And it only has 1 view, presumably from me, so someone please respond if they can see it. I couldn't find anything to change in privacy or whatever/

 

[Arijun]

My intuition says that it will be something like
cos(θ)[F_orig- v_xtan(θ)]
where F_orig = the force you would get on a flat surface
and v_x is your horizontal velocity.
I don't have any proof, but I can explain my reasoning:
The angle lessens the force because the normal force can only oppose the component of the force parallel to it (as in if I push an ice skater directly horizontally, his legs will only feel like they are supporting his weight, whereas if I push him at a downward angle, they will feel like they are supporting a little more) that is what the cosθ in front is for.
However, you are also moving forward, which means that as you land, you will not need to completely stop your vertical motion, simply reduce it enough to move down only a certain amount feet for every foot you move forward. Since force can also be considered a change in momentum, i.e. Mom_fin-Mom_init, you can change your final momentum to something a little closer to your initial momentum, thereby lessening your change in momentum and the force your legs feel.

 

[a_skier]

Hmmm, I worked through that and I got something still around 2000 pounds.

I think the problem with that equation may lie that you are subtracting the horizontal velocity, whereas shouldn't the horizontal velocity be combined with the angle of the slope to somehow find a percentage of the original force? I don't know the exact equations for this but I feel like we just have to find the proper way to express the horizontal velocity and the angle of the slope upon the basic force of impact. Some sort of ratio as to what percentage of the basic force of impact is taken away by horizontal velocity and the angle of the slope.

Let me know if you think of anything, I really appreciate the try!

 

[gneill]

You might consider an "impulse" approach, which considers the change in momentum over a short time period. If you can estimate the time that the landing takes from contact until you're moving downslope in a normal fashion, and estimate your downslope speed at the end of the impact, then the change in momentum can be determined. From that an average force can be extracted.

With a few wild guesses, estimating the impact to occur over 1/2 second, your mass to be about 180 lbs with skiing kit, and your post-impact speed downslope to be 10mph, that yields an average force of about 785 lbf. The associated acceleration at impact would be about 4.5 g's.

 

[PhanthomJay]

I am not sure how you arrived at 2000 pounds impact force without a knowledge of Physics and without giving your weight. if you were to jump sytraight down from rest with no initial forward or downward speed, you'd impact the snow at about 40 mph, and if you stopped after penetrating 3 feet of snoe, the impact force would be around 20 times your weight (4000 pounds if you weighed 200 pounds, or 2000 pounds if you weighed 100 pounds, etc.). But in your prob;em, many factors are involved, such as angle of impact with the 40 degree slope, forward speed, air resistance, whether you bend your knees, and whether you actually penetrate 3 feet of snow versus say 1 foot, while still maintaining your forward speed. The impact force may be less, but I haven't worked out any numbers or had time to attempt a soltion with assumptions.

 

[The Anonymous]

Never mind - I saw two glaring errors in my first reply. I'll try again later when I have more time.

 

[PhanthomJay]

Without running any numbers, I think that gneill's 'wild guess' may be in the ballpark. Surfing the Net, I found a pretty good website on snowboard jumping which applies to ski jumping as well. In some cases if your horizontal and vertical speed at impact result in a velocity vector parallel to the slope, you may experience a normal force less than your weight! In your case, it looks like you won't be hitting parallel to the slope, so your impact force will be greater than your weight. This site contains a lot of Physics, but nonetheless makes for an interesting read. Toward the end it talks about jumping onto a slope with a horizontal component of velocity.

http://physik.uibk.ac.at/04-05/erde/spezial/aufgaben/snowboard%2Blanding_force.pdf