A broom balances at point x 1 fromits upper end. When a weight of mass m is atta
ID: 1496336 • Letter: A
Question
A broom balances at point x1 fromits upper end. When a weight of mass m is attached at its upper end, the point of balance shifts to x2.
a. Find an expression for the weight of the broom.
b. What is the weight of the broom if m=.23 kg, x1=.940 m and x2= 1.10 m?
Hint: Recall that in the expression for the position of the center of mass, the integral represents a sum over all the parts of the object in question. If another part is added then the sum is replaced by the sam sum plus an extra term consisting of an integral over the added volume. If the extra part is discrete that can be modeled as a point mass, then the extra term will consist of the mass of the object multiplied by its position.
Explanation / Answer
mass of the broom = M
cm of broom = x1
mass added = m
cm of broom+mass = x2
about the center of mass
m*x2 = M*(x2-x1)
+++++++++++++++++++++++++
partb
M = 0.23*1.1/(1.1-0.94)
M = 1.58 kg
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