Distance from the Center of Gravity of a Object
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 11.3 kg and 1.00 m long and the right one is 41.0 kg and 2.00 m long.
How far from the left end of the left beam is the center of gravity of the object?
x = center of gravity
m = mass of each beam
m1= 11.3 kg
m2= 41.0 kg
d = distance from the left side to the middle. (center of gravity)
left beam, d = (1/2)(1.00 m) = 0.5 m
right beam, d = 1.00 m + (1/2)(2.00m) = 2.0 m
x = (Σmd) / (Σm)
x = [(11.3)(0.5) + (41.0)(2.0)] / (11.3 + 41.0)
x=(5.65 + 82)/52.3
x = 1.68m
2) What is the gravitational torque on the object about an axis through its left end?
τ = (m1 + m2)(g)(x)
*note gravity is s downward force, so it is negative
τ = (11.3 kg + 41.0 kg)(-9.81 m/s²)(1.68 m)
τ = -859 N·m