1) Julie has been hired to help paint the trim of a building, but she is not con

Question

1) Julie has been hired to help paint the trim of a building, but she is not convinced of the safety of the apparatus. A 5.6 m plank is suspended horizontally from the top of the building by ropes attached at each end. She knows from previous experience that the ropes being used will break if the tension exceeds 1.0 kN. Her 97 kg boss dismisses Julie's worries and begins painting while standing 1.0 m from the end of the plank. If Julie's mass is 50 kg and the plank has a mass of 15 kg, then over what range of positions can Julie stand to join her boss without causing the ropes to break?

0 < x <

_____________ m (where x is measured from the end furthest from Julie's boss)

Explanation / Answer

Let TL and TR be the tensions on the left and right ropes.

Summing forces,

TL + TR - [mboss + mJulie + mplank]g = 0

Thus,

TL + TR = 1587.6 N    [1]

Summing torques, using the right end [farther from the boss] as the pivot,

TL (5.6 m) - mboss g (4.6 m) - mplank g (2.8 m) - mJulie g x = 0

Solving for TL in terms of x,

TL = 854.35 - 87.5 x

Substituting this to   [1],

854.35 - 87.5 x + TR = 1587.6 N

Thus,

TR = 733.25 + 87.5x < 1000 N

Solving for x,

0< x < 3.049 m   [ANSWER]

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