What is the distance at which the bobsled will come to a halt?

[mikefitz]

http://img76.imageshack.us/img76/6271/pichp1.gif

A bobsled run leads down a hill as sketched in the figure above. Between points A and D, friction is negligible. Between points D and E at the end of the run, the coefficient of kinetic friction is µk = 0.4. The mass of the bobsled with drivers is 210 kg and it starts from rest at point A.

Find the distance x beyond point D at which the bobsled will come to a halt.

I'm thinking the best way to approach this problem is by calculating the final speed of the bobsled (bottom of the 2nd hill) and using the mass and µk to come up with the distance.

I'm having trouble visualizing how to come up with the final speed, however. The second hill is 30m high, but the initial speed down the hill will not be 0 due to the speed the bobsled gains from the first 50m hill. Where should I begin? Thanks

 

[Doc Al]

Hint: Since there's no friction between A and D, what is conserved?

 

[mikefitz]

So, since the external forces are 0 then total energy does not change from one place to the next.

energy at top = energy at bottom

But how do the 50m and 30m heights effect the speed of the sled? or do they? thanks again

 

[Doc Al]

So, since the external forces are 0 then total energy does not change from one place to the next.

energy at top = energy at bottom

Since dissipative forces are zero, the total energy is conserved.

But how do the 50m and 30m heights effect the speed of the sled? or do they?

They certainly affect the speed of the sled as it goes over those hills, but no energy is lost. Those hills don't affect the speed at D.