Question

If a skiier falls and begins sliding down the hill, and her speed at the bottom of the hill depends on: speed at the time of the fall, length of the hill and steepness of the hill. Why is weight not included? Wouldn't the forces acting on her be friction + gravitation (hence weight)?

Answer 1

because you can solve the question using kinematics or dynamics. Kinematics never includes mass. Though, kinematics and dynamics are tied together by the inclusion of acceleration in certain kinematic equations. You could use the variables mentioned (speed at time of fall...etc) in order to determine whatever you want/can. Then, using the acceleration you eventually solve for (if that is what you want to solve for) you can determine the forces acting on the object, but you don't NEED forces so long as you have kinematic variables with which to determine how the motion will evolve. If you need a diagram let me know and I will be happy to make you one.

Answer 2

I'm still confused. sure, you can use kinematics to solve for it, but what if you wanted to look at it using forces?

Answer 3

you could of course solve the problem using forces, you would just be complicating the situation needlessly.

Answer 4

I personally always lean toward the dynamics aspect of things, but I have always been told that I made my life a bit harder than it should be. However, if working with forces allows you to things more clearly, GO FOR IT!

Actually even when you take into consideration drawing a force diagram you will quickly notice that the mass cancels out of the system. Remember you have gravity, friction, your normal, and the intial momentum of your skier when he/she falls. You will need to remember that you are dealing with an incline surface(This is basically an incline plane problem).

Answer 5

If you look at it using forces, observe a free-body diagram. The net forces acting on the skier are from gravity, the normal force, and friction (if there is friction). By using axes that have the positive x direction in the direction of the momentum, you can find the forces acting in the x direction, which, using the momentum principle, will allow you to find the velocity. This also, creates a situation where, in the x direction, the only force is gravity.
\[dp/dt = Fnet = mdv/dt = -mg \cos \theta \]
Theta comes from the steepness of the hill. You will notice that you can divide out the mass of the skier.