A massless, rigid board is placed across two bathroom scales that are separated by a distance of 1.71 m. A person lies on the bo
ard. The scale under his head reads 475 N, and the scale under his feet reads 316 N. (a) Find the weight of the person. (b) Locate the center of gravity of the person relative to the scale beneath his head.
1 answer:
Answer:
Let the weight of the person be W and be located at a distance 'a' from the left scale as shown in the figure
Since the body is in equilibrium we can use equations of statics to analyse the problem.
Taking Sum of Moments about A we have
Taking Sum of Moments about B we have
Solving the above 2 equations for W and 'a' we get
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Answer:
(a) I_A=1/12ML²
(b) I_B=1/3ML²
Explanation:
We know that the moment of inertia of a rod of mass M and lenght L about its center is 1/12ML².
(a) If the rod is bent exactly at its center, the distance from every point of the rod to the axis doesn't change. Since the moment of inertia depends on the distance of every mass to this axis, the moment of inertia remains the same. In other words, I_A=1/12ML².
(b) The two ends and the point where the two segments meet form an isorrectangle triangle. So the distance between the ends d can be calculated using the Pythagorean Theorem:
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Finally, using the Parallel Axis Theorem, we calculate I_B: