In the sport of skeleton a participant jumps onto a sled (known as
a skeleton) and proceeds to slide
down an icy track, belly down and
head first. In the 2010 Winter
Olympics, the track had sixteen turns
and dropped 126 m in elevation from
top to bottom. (a) In the absence of
nonconservative 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 at
the beginning of the run is relatively
small and can be ignored. (b) In reality, the gold-medal winner (Canadian
Jon Montgomery) reached the bottom
in one heat with a speed of 40.5 m/s
(about 91 mi/h). How much work was
done on him and his sled (assuming a
total mass of 118 kg) by nonconservative forces during this heat?
I successfully finished part a.) and came up with Vf=49.7m/s. Part b.)is where I need help.
To calculate the work done by nonconservative forces on the skeleton rider and sled, you can use the work-energy theorem. The work-energy theorem states that the work done on an object is equal to the change in its kinetic energy.
In this case, we can assume that the only nonconservative force acting on the rider and sled is friction, which opposes their motion. Therefore, the work done by friction can be calculated using the equation:
Work = Change in Kinetic Energy
Since the speed at the beginning of the run is relatively small and can be ignored, we can assume that the initial kinetic energy is zero. Thus, the work done by nonconservative forces can be written as:
Work = Final Kinetic Energy - Initial Kinetic Energy
The final kinetic energy of the rider and sled can be calculated using the equation:
Kinetic Energy = (1/2) * mass * velocity^2
Substituting the values given:
Mass (m) = 118 kg
Velocity (v) = 40.5 m/s
Final Kinetic Energy = (1/2) * 118 kg * (40.5 m/s)^2
Now, you can calculate the work done by nonconservative forces by substituting the final kinetic energy and initial kinetic energy (which is zero) into the work equation:
Work = (1/2) * 118 kg * (40.5 m/s)^2 - 0
Simplifying the equation will give you the work done by nonconservative forces on the rider and sled during the heat.
To solve part b), we need to determine the work done on the participant and their sled by nonconservative forces, such as friction and air resistance. The work done by these forces is equal to the change in mechanical energy.
The initial mechanical energy (Ei) of the participant and sled is given by:
Ei = mgh
Where:
m = total mass of the participant and sled (118 kg)
g = acceleration due to gravity (approximately 9.8 m/s^2)
h = height of the track (126 m)
The final mechanical energy (Ef) of the participant and sled is:
Ef = 1/2 mvf^2
Where:
vf = final speed of the participant and sled (40.5 m/s)
The work done by nonconservative forces (W_nc) is:
W_nc = Ef - Ei
Substituting the equations for Ei and Ef, we have:
W_nc = 1/2 mvf^2 - mgh
Substituting the given values:
W_nc = 1/2 * 118 kg * (40.5 m/s)^2 - 118 kg * 9.8 m/s^2 * 126 m
Calculating the expression above will give us the work done on the participant and their sled by nonconservative forces during the heat.