SUSPENDING AN OBJECT

Problem

An object weighing 1 unit is suspended by three wires attached to three hooks on a horizontal ceiling. We have chosen our axes so that the ceiling is the xy plane and the z axis points up. The hooks are placed at the points A(0,0,0), B(1,0,0), and C(0,2,0) - the distances are measured in metres. Suppose the lengths of the wires from the object to the hooks A,B,C are a,b,c metres respectively.

1. Determine the coordinates of the object. Does this make sense for all values of a,b,c?
2. Determine the tension in each of the strings.
3. What conditions must be satisfied by a,b,c for all three strings to be taut?
4. Will the object hang with all strings taut if a=2, b=2, c=2.5? Justify your claim.

Suggestions

• You will probably need Maple to solve this problem but don't go near a computer until you have come up with a strategy (using pencil and paper) to solve this problem.
• You may wish to use a few of the vector related commands described in Section 3 of the tutorial.
• Start work on this problem right away. There isn't much time.
• You will probably not finish your work in one Maple session. Save your work to be able to use it later.
• Points will be deducted for poorly presented solutions and poorly commented output.

 
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