Center of Mass problem help! A man with mass mj = 58 kg stands at the left end o

Question

Center of Mass problem help!

A man with mass mj = 58 kg stands at the left end of a uniform boat with mass m2 = 161 kg and a length L = 3.3 m. Let the origin of our coordinate system be the man's original location as shown in the drawing. Assume there is no friction or drag between the boat and water. What is the location of the center of mass of the system? If the man now walks to the right edge of the boat, what is the location of the center of mass of the system? After walking to the light edge of the boat, how far has the man moved from his original location? (What is his new location?) Now the man walks to the very center of the boat. At what location does the man end up?

Explanation / Answer

as there is no external force , centre of mass remains constant

so intial COM = (3.3 * 161/2)/(58 +161) = 1.21 m

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Centre of Boat = 1.21 - (3.3/2 -1.21)

Centre of Boat = 0.77 m

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Mid of the boat is as 1.21 m

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The center of mass of the boat has moved to the left by

dx = (3.3/2)/(1 + m(boat)/man)

dx = 3.2/3 /(1+161/58)= 0.282 m

to the left from its original position.

(3.3/2) - 0.282 = 1.38 right side from the origin.

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5) ds = (3.3/2)/(1+58/161) = 1.21 m to the left

The displacement of the man is given by dx = s/(1 + m(man)/m(boat))

dx = (3.3)/(1+58/161) = 2.42 m to the right from the origin

the new position of man = 2.42 -1.21 = 1.21 m to the right of the origin

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