How much upward force does support 1 and support 2 exert on the beam?

A 3.0-m-long rigid beam with a mass 110 kg is supported at each end. An 90 kg student stands 2.0 m from support 1.

3 Answers

  • 110 x 9.8 = 1078 N

    90 x 9.8 = 882 N

    T1 = (1078 x (3/2)) + (882 x 1) = 2499

    2499 = 3T1

    2499/3 = T1 = 833 N (support 1)

    T2 = (1078 x (3/2)) + (882 x 2) = 3381

    3381 = 3T2

    3381/3 = T2 = 1127 N (support 2)

  • weight of beam = (110)(9.81) = 1079 N

    this weight is shared (equally) by each support = 1079/2 = 539.55 N

    weight of student = (90)(9.81) = 882.9 N

    882.9 is shared 1/3 to 2/3 between supports 1 & 2:

    support 1 => 882.9/3 = 294.3 N

    support 2 => 882.9(2/3) = 588.6 N

    Total Load Bearing is:

    support 1 = 294.3 + 539.55 = 834 N ANS

    support 2 = 588.6 + 539.55 = 1130 N ANS

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