Question

1. A bobsled and passenger with a total mass of M make a run starting from rest down an ice track that is H meters vertical distance from top to bottom where the race ends and the bobsled reaches a speed v1. The sled then continues moving but slows to rest along a high friction, horizontal section of track of length L.

a)Describe the forms and change of forms of energy the bobsled and passenger have in what parts of their journey, beginning from the start of their run through the end of the race and until they come to a stop.

b) Is the energy of the bobsled and passenger conserved for the entire trip, for part of the trip, or for no part of the trip? If it is conserved for part of the trip, which part(s)?

c) Derive an equation, showing all of your steps, for the speed v, of the sled at the bottom of the hill in terms of other given variables and constants such as M, H, g, L. Not all variables may be required.

d) Derive an equation, showing all of your steps, for the average force of friction acting on the bobsled, in terms of M, H, g, L, and/or V1. Not all variables may be required.

Answer 1

The bobsled's energy changes from gravitational potential energy to kinetic energy during its descent and is later dissipated as heat and sound due to friction. Conservation of energy applies only to the descent without friction. The speed and force of friction can be calculated using the principles of conservation of energy and the work-energy principle, respectively.

Energy Changes in a Bobsled Run

At the start of the bobsled run, the bobsled and its passenger have gravitational potential energy due to their height H above the end of the track. As the sled descends, this potential energy is converted into kinetic energy, resulting in the sled reaching a speed v1 at the bottom of the hill. The energy transformation here follows the principle of conservation of energy, where the initial potential energy equals the final kinetic energy minus any work done by non-conservative forces (in this scenario, ideally, none).

On the high friction, horizontal section of the track, the kinetic energy is transformed into heat and sound due to the work done by the force of friction. Energy is not conserved in this part of the journey because it is dissipated through non-conservative forces (friction). To derive an equation for v1, we apply conservation of energy: MgH = 0.5Mv1^2, leading to v1 = sqrt(2gH), with g being the acceleration due to gravity.

To calculate the average force of friction f_avg, we can use the work-energy principle: the work done by friction, which equals the force of friction times the distance L, must be equal to the initial kinetic energy of the sled: f_avg \* L = 0.5 \* M \* v1^2. Therefore, f_avg = (0.5 \* M \* v1^2) / L.