Physics 166 Lab I

 

  1. Users Tour: take  tour of Maple (Maple 10).
    1. Ten Minute Tour
    2. Numeric and Symbolic Computations
    3. Simple problems

1) Two logs, each of weight W, lie in a trough with vertical walls in such a way that when viewed end-on the line between their centers makes an angle q with the horizontal. The magnitude of the forces on the bottom log due to the top log, the bottom of the trough, and one wall on the trough are F12, F1b, and F1w, respectively. Similarly the forces on the top log due to the bottom one and the other wall are F21 and F2w. Since F12 = F21, three equations for static equilibrium are

            -F12 cos(q) + F1w = 0

            F1b - W - F12 sin(q) = 0

            F12 cos(q) - F2w = 0

Assuming that all frictional forces are negligible. Find a fourth equation and use Maple to

    1. Find the magnitude of the forces F12, F1b, F1w, and F2w. That is find the forces in terms of W and q.
    2. Check the solutions
    3. Verify the q ® p/2 limits for the forces.
    4. (Optional- if you are done really quickly and are bored) Plot the forces vs q.

This second problem is for you to do for fun after class - you do not have to hand it in

2) A mass M is supported by three wires, as shown below. Two equations for static equilibrium are

T - Mg = 0

T1 sin(q1) + T2 sin(q2) - T = 0

where T, T1, and T2 are the tensions in the three wires.

      1. Find a third equation and find the tensions using Maple.
      2. Show that the tensions can be written

T1 = (Mg cos(q2))/sin(q1+ q2), T2 = (Mg cos(q1))/sin(q1+ q2)

c. Show that in order to support the mass when the two angles are negligibly small the tensions T1 and T2 must be infinitely large.