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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.
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b) Taking the left-most point of the beam as the pivot determine which forces lead to clockwise (negative) and counter-clockwise (positive) rotations.
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Clockwise: Counter-Clockwise:
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c) Write down the relation that expresses the fact that the beam is in rotational equilibrium.
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d) Solve the equation of part (c) for the mass m that is needed to keep the rod balanced.
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e) Using M = 0.5 kg, the mass of the beam at your table, and d = 2L/3, solve for a value for m.
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=
)
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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?
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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?
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3.
a)
Write out the translational equilibrium equations for the beam, as
derived from your free-body diagram in (1a).
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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.
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