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A barbell is 1.5 m long. Three weights, each of mass 20 kg, are hung on the left and two weights of the same mass, on the right. The width of each weight is 4 cm and each group of weights is placed 4 cm from the ends. Where is the center of mass of the barbell as measured from the mid-point, M, of the bar? The bar is of uniform mass and has mass 5 kg, and the retaining collars are of negligible mass. Take to the right as positivea. -5.90cmb. -11.6cmc. +13.7cmd. +5.90cme. none of the above

User LanceSc
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4 votes

Answer:

b. -11.6 cm

Step-by-step explanation:

We have given parameters:

Length, l = 1.5 m = 150 cm

Mass of weight,
m_1 = 20 kg

Width, x = 4 cm

Distance d = 4 cm

Mass of bar,
m_(bar) = 5 kg

We are asked to find the center of mass from the mid-point,
X_(CM) = ?

Since 3 weights are on the left and 2 weights are on the right, we know:


m_(left) = 3 * 20 = 60 kg


m_(right) = 2 * 20 = 40 kg

And also we know that,
M = (l)/(2) = 150/2 = 75 cm

For the left side, center of mass is:


x_(left) = (3 * 4)/(2) = 6 cm

From the midpoint, the distance to the left is:


X_(left) = -(M - 4 - x_(left)) = -(75 - 4 -6) = -65 cm

For the right side, center of mass is:


x_(right) = (2 * 4)/(2) = 4 cm

From the midpoint, the distance to the right will be:


X_(right) = (M - 4 - x_(right)) = (75 - 4 - 4) = 67 cm

Hence,


X_(CM) = (m_(right)*x_(right) + m_(left)*x_(left) )/(m_(right) + m_(left) + m_(bar)) = (40 * 67 - 60 * 65)/(40 + 60 + 5) = -11.62 cm

User Landon Statis
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