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.
Your question is incomplete.
To design a Bobsled Run for the Walrus of Fun theme park, there are several steps you need to follow:
1. Determine the length of the track:
The maximum length allowed is 1500 meters, but you can use less if needed.
2. Decide on the number and characteristics of hills:
You need to include a minimum of three hills. You have the freedom to choose the steepness (angle) and height of each hill.
3. Plan the turns:
You need to include two turns in the track to complete one lap. The coefficient of friction around the turns is zero. You need to select the radius of curvature for each turn and determine the angle at which the turns should be banked to keep the sled on the track.
4. Create a sketch:
Draw a neat side view and top view of your bobsled track, clearly indicating the heights of the hills, lengths of any straightaways, and the lengths of the track for the hills. Label all the details.
5. Consider the initial acceleration and tension:
There is a massless cable on a frictionless pulley that pulls the bobsled car to the top of the first hill with a given acceleration. Determine the tension in the cable, work done by the cable, and work done by friction in dragging an empty and fully loaded sled to the top of the first hill.
6. Determine the initial velocity at the first hill:
Since the sled had an acceleration going up the first hill, it will have an initial velocity when reaching the top. Calculate this velocity assuming the sled started from rest.
7. Calculate work done by friction:
Determine the work done by friction going up each hill, down each hill, and along any straightaways for a fully loaded sled. Label these clearly either on your drawing or on a separate sheet. Show all calculations.
8. Calculate velocities at different points:
Determine the velocity at the top and bottom of each hill, as well as at the beginning and end of each straightaway. Label these clearly either on your drawing or on a separate sheet. Show all calculations.
9. Determine banking angle for turns:
Based on the velocity of the sled going into each turn, calculate the angle required to "bank" the turn and keep the car on the track.
10. Determine track length for stopping:
Based on the velocity of the sled coming into the final straightaway before it stops, calculate how much track is needed for the frictional forces to bring the sled to a safe stop.
11. Neatly label side view and top view:
Provide a neatly labeled side view of your track, including heights, lengths, and hill tracks. Also, provide a neat top view that shows the radius of curvature for the turns.
By following these steps and performing the necessary calculations, you can design a Bobsled Run for the Walrus of Fun theme park in Anchorage, Alaska.