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Monday, March 22nd, 2010
TA: Tomoyuki Nakayama
PHY 2048: Physic 1, Discussion Section 3705
Quiz 7 (Homework Set # 10)
Formula sheets are not allowed. Calculators are allowed. Do not store equations in your calculator.
You need to show all of your work for full credit.
In the figure below right, one end of a uniform beam of weight 300 N is hinged to a wall; the other
end is supported by a wire that makes angles θ = 25.0º with both wall and beam.
a) Draw all the forces exerted on the beam in the figure, and write down the translational equilibrium
conditions (balance of forces equations) and rotational equilibrium condition (balance of torques
equation) for the beam.
Four forces are exerted on the beam: x and y components of the resistive force from the hinge,
tension force from the wire and the gravitational force. Applying the translational equilibrium
condition along the x and y axes, we get
Rx - Tcosθ = 0
Ry + Tcosθ – W = 0
Choosing our rotational axis at the hinge, the rotational equilibrium condition
-W(L/2)sin(2θ) + TLsinθ = 0
Note that the angle between the beam and –y axis is 2θ, for this is the exterior
angle opposite the two vertices of angle θ and θ.
b) Find the tension in the wire.
Solving the balance of torques equation in part a), we get
T = Wsin(2θ) /(2sinθ) = 300 × sin50º / (2sin25º) = 272 N
c) Find the horizontal and vertical components of the force of the hinge on the beam.
We solve the balance of forces equations in part a), we get
Rx = Tsinθ = 272 × sin25º = 115 N
Ry = W-Tcosθ = 300 - 272cos25º = 53.5 N