A machine part consists of a thin, uniform 4.00-kg bar that is 1.50 m long, hing

Question

A machine part consists of a thin, uniform 4.00-kg bar that is 1.50 m long, hinged perpendicular to a similar vertical bar of mass 3.00 kg and length 1.80 m. The longer bar has a small but dense 2.00-kg ball at one end (Figure 1)

Part A

By what distance will the center of mass of this part move horizontally and vertically if the vertical bar is pivoted counterclockwise through 90 to make the entire part horizontal?
Find the magnitude of horizontal displacement.

Part B

Find the direction of horizontal displacement.

Part C

Find the magnitude of vertical displacement.

Part D

Find the direction of vertical displacement.

I am stuck on what to do. Thanks!

Explanation / Answer

let com be (x,y)
and let the origin be at the hinge
then (x,y) = ([4*(-0.75)+3*0 + 2*0]/(4+3+2),[4*0 + 3*(-0.9) + 2*(-1.8)]/(4+3+2)) = (-0.33,-0.7)

a) New com (x,y) = ([4*(-0.75) + 3*0.9 + 2*1.8]/9 , 0) = (0.366,0)
distance moved by x com = 0.366+0.33 = 0.699
distance moved by y com = 0.7
b) Direction of horizontal displacement = towards positive x axis
c) Magnitude of vertical displavement = 0.7
d) Direction of vertical displacement = towards +ve y axis

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