Starting at the top of a steep, icy track, a rider jumps onto a sled (known as a skeleton) and proceeds - belly down and head first - to slide down the track. The track has fifteen turns and drops 104 m in elevation from top to bottom. (a) In the absense of non-conservative forces, such as friction and air resistance, what would be the speed of a rider at the bottom of the track? Assume that the speed of the rider at the beginning of the run is relatively small and can be ignored. (b) In reality, the best riders reach the bottom with a speed of 35.8 m/s (about 80 mi/h). How much work is done on an 93.2-kg rider and skeleton by non-conservative forces?

Wnc=change in energy=ef-eo

=.5mvf^2 - mgh
Should get -32540.68 J

i found that part a) is 45.1 m/s but i don't kno how to find part b)

(a) To find the speed of the rider at the bottom of the track in the absence of non-conservative forces, we can use the principle of conservation of mechanical energy.

The potential energy at the top of the track can be calculated using the equation: Potential Energy = mass * gravity * height.

In this case, the mass of the rider and skeleton is not given, but we can assume it to be m. The height is given as a drop of 104 m, and acceleration due to gravity is 9.8 m/s^2.

Potential Energy at the top = m * 9.8 m/s^2 * 104 m

At the bottom of the track, all the potential energy will be converted into kinetic energy. Therefore, we can equate the potential energy at the top to the kinetic energy at the bottom.

Potential Energy at the top = Kinetic Energy at the bottom

m * 9.8 m/s^2 * 104 m = (1/2) * m * v^2

Simplifying the equation, we can solve for the speed (v):

v^2 = (2 * 9.8 m/s^2 * 104 m)

v = sqrt(2 * 9.8 m/s^2 * 104 m)

v ≈ 45.28 m/s

Therefore, the speed of the rider at the bottom of the track in the absence of non-conservative forces would be approximately 45.28 m/s.

(b) To find the work done on the rider and skeleton by non-conservative forces, we need to determine the change in kinetic energy.

Change in Kinetic Energy = Final Kinetic Energy - Initial Kinetic Energy

Assuming the initial speed is zero (as given in the question), the Initial Kinetic Energy is 0.

The Final Kinetic Energy is calculated using the equation: Kinetic Energy = (1/2) * mass * velocity^2.

Given the final speed as 35.8 m/s, and mass as 93.2 kg, we can calculate the Final Kinetic Energy:

Final Kinetic Energy = (1/2) * 93.2 kg * (35.8 m/s)^2

Now, the work done by non-conservative forces is equal to the change in kinetic energy:

Work = Final Kinetic Energy - Initial Kinetic Energy

Work = (1/2) * 93.2 kg * (35.8 m/s)^2 - 0

Calculating the above expression will give us the work done on the rider and skeleton by the non-conservative forces.