Posted by Ashley on Monday, March 17, 2008 at 12:17am.
Lucky you have been commissioned to design a Bobsled Run for the new theme park Walrus of Fun going up in Anchorage, Alaska. You get a maximum of 1500 meters of track to work with. Except on the turns the coefficient of kinetic friction is .15.
Here is what you need to have:
1. 1500 m of track (maximum) for the entire run. You may use less track if needed.
2. A minimum of three hills. You will decide how steep (angle) and how high you want each of the hills.
3. There will be two turns so the track makes one lap. The coefficient of friction around the turns is zero. You will decide the radius of curvature of the turns. You will also have to decide the angle you should bank your turn to keep your sled on the track.
4. You will include a neat sketch of the side view and top view of your bobsled track.
5. There is a massless cable on a frictionless pulley that pulls your bobsled car to the top of the first hill with an acceleration of .
6. The mass of the sled is 350 kg. It can contain 2 people for a maximum mass of 600 kg.
7. Due to OSHA standards and safety reasons, your sled must never exceed 25 m/s.
8. A “natural” braking system of crunchy snow and ice is on the track at the end of the run. The coefficient of friction for this patch of track is .3
Here is the grading:
1. (5 points) Determine the Tension, Work done by the cable, and Work done by friction in dragging an empty and fully loaded sled to the top of your first hill.
2. (5 points) Since the sled had an acceleration going up that first hill, it has an initial velocity upon reaching the first hill. Determine that velocity assuming the sled started from rest.
3. (25 points) Determine the work done by friction going up each hill, down each hill, and along any straightaway of a fully loaded sled. Label these clearly either on your drawing or on a separate sheet. Show ALL calculations
4. (25 points) Determine the velocity at top and bottom of each hill, and at the beginning and end of each straight away. Label these clearly either on your drawing or on a separate sheet. Show ALL calculations.
5. (10 points) Based on the velocity of your sled going into each turn, determine the angle required to “bank” the turn to keep your car on the track.
6. (10 points) Based on the velocity of your sled coming into the final straightaway before it stops, determine how much track is needed for the frictional forces to do their work and bring that sled to a safe stop.
7. (10 points) Neatly labeled side view of your track. Make sure heights of the hills, lengths of any straightaway, and the lengths of track of your hills are labeled.
8. (10 points) Neatly labeled top view that shows the radius of curvature of your turns.
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