Two thin beams are joined end-to-end as shown in the figure to make a single obj
ID: 2259644 • Letter: T
Question
Two thin beams are joined end-to-end as shown in the figure to make a single object. (The object is seen from the side.) The left beam is 11.9kg and 1.00 m long and the right one is 40.5kg and 2.00 m long
How far from the left end of the left beam is the center of gravity of the object?
What is the gravitational torque on the object about an axis through its left end?
Explanation / Answer
x = (?md) / (?m)
x = centroid (center of gravity)
m = mass of each beam = 11.9 kg, 40.5 kg
d = distance from the left side to the center of gravity of each beam. Assume it's in the middle.
For the left beam, d = (1/2)(1.00 m) = 0.5 m
For the right beam, d = 1.00 m + (1/2)(2.00m) = 2.0 m
x = [(11.9)(0.5) + (40.5)(2.0)] / (11.9 + 40.5)
x = 1.659 m
T = Fd
T = torque
F = force = mg
d = distance
Torque can be dtermined by two ways here :
either find the torque of each force individually and add them,
or find the torque from the combined weight through the centroid.
T = (11.9 kg + 40.5 kg)(9.81 m/s^2)(1.659 m)
T = 852.799 N
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