# The Bobsleigh event

The "bobsleigh" is just a fancy sled. Teams of two or four athletes push the sled from a standing start, then jump into it and coast down to the bottom of the track. The total mass of the sled plus its crew is limited to M = 630 kg for 4-man teams, or 390 kg for 2-man teams.

At the 2006 Torino games, competitors are sliding down a track built in Cesana, Italy. Click on the image below for a larger, annotated version.

Some details of this track:

```
Length:           1,435 m
Start Altitude:   1,683 m
Finish Altitude:  1,569 m
Number of Curves:    19
```

1. Under ideal conditions, what is the maximum speed a sled could reach at the end of the track?
2. How much work does gravity do on a 4-man sled during the race?
3. Under ideal conditions, which should take less time to run the race: a 2-man sled or a 4-man sled? Explain.
4. Under realistic conditions, which should take less time to run the race: a 2-man sled or a 4-man sled? Explain.
5. The top speed of the sleds is about v = 36 m/s. When a sled moving at that speed goes around the turn labelled "T" above, what is its centripetal acceleration? Express your answer in m/s^2 and in gees.
6. Suppose the actual speed at the finish line is about 30 m/s. How much work has friction done on the sled?
7. Estimate the coefficient of kinetic friction between sled and ice.
8. During the start, a 4-man team pushes the empty sled (mass about 250 kg) a distance of about 65 meters in about 5 seconds. What is the average acceleration of the sled during the start? What is the average force exerted on the sled by the team?