1. Consider a beam of length L that is hinged at one end and supported by a cord at the other as shown in the figure. Suppose a mass M is hung at a distance of d from the hinge and that the supporting cord makes an angle of q = 30° with the horizontal. Attached to the other end of the cord is a mass m. Take the mass of the beam mB to be equal to the value on the beam at your table.
a) Draw a free-body diagram for the beam.
b) Taking the left-most point of the beam as the pivot determine which forces lead to clockwise (negative) and counter-clockwise (positive) rotations.
c) Write down the relation that expresses the fact that the beam is in rotational equilibrium.
d) Solve the equation of part (c) for the mass m that is needed to keep the rod balanced.
e) Using M = 0.5 kg, the mass of the beam at your table, and d = 2L/3, solve for a value for m.
2. Using the beam and masses at your table, set up the mass-beam configuration of the proceeding problem.
a) Use the protractor provided to set the angle q = 30°. Obviously, you will not be able to set the angle at precisely this value – can you estimate your percentage error?
b) Taking M = 0.5kg experimentally determine the mass m required to balance the beam. How does this compare with your answer to (1e)? How are your errors related to your uncertainties in your measurements?
3. a) Write out the translational equilibrium equations for the beam, as derived from your free-body diagram in (1a).
b) Solve for the reaction force R from the hinge on the beam by solving for Rx and Ry, drawing a vector diagram with them and solving for the magnitude and direction of R.