A uniform plank of weight 100 N is 2000 mm long and rests on a support that is 400 mm from end E. At what distance from E must a 160 N weigh

Question

A uniform plank of weight 100 N is 2000 mm long and rests on a support that is 400 mm from end E. At what distance from E must a 160 N weight be placed in order to balance the plank?

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Yến Oanh 4 years 2021-07-26T23:20:36+00:00 1 Answers 189 views -1

Answers ( )

  1. ngockhue
    0
    2021-07-26T23:22:16+00:00
    Reply

    Answer:

    the location of 160 N from end E is 25mm

    Explanation:

    given:

    A uniform plank of weight 100 N is 2000 mm long

    and rests on a support that is 400 mm from end E

    find:

    At what distance from E must a 160 N weight be placed in order to balance the plank?

                                                                          160 N

                                                                               |—x—>|

                                          100N                           \|/

    ======================||======================E

                                                                Δ—- 400mm—->|

    |<—————————-  2000mm   —————————>|

    to determine the location of 160N load in order to balance the plank,

    you have to take moment at support Δ.

    note:

    the 100 N is located at the center of a plank.

    the distance of 100N from support = (2000 / 2) – 400 = 600mm

    ∑moment at Δ = 0

    0 = -100 N (600mm) + 160 N (400-x)

    0 = -60000 N.mm + 64000 N.mm – 160x N.mm

    0 = 4000 – 160x

    160x = 4000

    x = 4000/160

    x = 25 mm

    therefore,

    the location of 160 N from end E is 25mm

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