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

Question

Julie has been hired to help paint the trim of a building, but she is not convinced of the safety of the apparatus. A 4.5 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 100 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 56 kg and the plank has a mass of 19 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

Here ,

mass of julie , mj = 56 Kg

mass of plank , mp = 19 Kg

T = 1 kN = 1000 N

mass of boss , mB = 100 Kg

let the distance from end is x

Balancing the moment of forces about the string away from her boss

4.5/2 * 19 * 9.8 + 100 * 9.8 * (4. 9 - 1) + 56 * 9.8 * (x) - 4.9 * 1000 = 0

solving for x

x = 1.915 m

hence , the range of positions for julie can stand is 0 < x < 1.915 m

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