Two thin beams of negligible width are joined end to end as shown. The mass and

Question

Two thin beams of negligible width are joined end to end as shown. The mass and length of the beams are shown.

A) Find the center of gravity of the two joined beams.
Express your answer in the form (x,y), taking the
origin at the bottom marked by a dot.

Two thin beams of negligible width are joined end to end as shown. The mass and length of the beams are shown. A) Find the center of gravity of the two joined beams. Express your answer in the form (x,y), taking the origin at the bottom marked by a dot. B) Calculate the gravitational torque on the joined beams about an axis through the marked origin.

Explanation / Answer

As centre of mass can be calculated by

Rcm=(M1R1+M2R2)/(M1+M2)

where R1 and R2 are centre of masses of M1 and M2 respectively

R1=0 i +7.5 j

R2=2.5 i +15 j

35*Rcm=M1R1+M2R2

35*Rcm =15(0 i +7.5 j)+20(2.5 i +15 j)

35*Rcm =50 i + 412.5 j

Rcm =1.4285 i + 11.785 j

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