Question

(17%) Problem 4: A painter (of mass 71 kg) needs to reach out from a scaffolding to paint the side of a building, so he lays a plank across two bars of the scaffolding, and puts a heavy bucket of mass 67 kg directly over one of the bars (see figure). You can assume the plank is massless, and is long enough to reach to the other building. L d ©theexpertta.com If the bars are separated by a distance 1.1 m, how far, d, from the bar on the the right can the painter walk before the plank starts to fall? Grade Summary d= Deductions Potential 100% 0% п ( 7 8 9 HOME E 4 5 6 sin cos cotan asino atan acotan cosho tanh Degrees tan acos sinh colanh) Radians Submissions Attempts remaining: 70 (3% per attempt) detailed view 1 2 3 + - 0 END vo BACKSPACE CLEAR Submit Hint Feedback I give up! Hints: 0% deduction per hint. Hints remaining: 2 Feedback: 0% deduction per feedback.

Answer 1

Mass of painter = Mp = 71 kg

Mass of bucket = Mb = 67 kg

distance between bars = L = 1.1 m

For the momet just before which the painter is about to fall, the distnace d would be such that the plank is just about to lose contant with the leftmost bar so that the plank topples over

For this to happen, we need to determine minimumm value of d for which the vertical reaction at leftmost bar is zero and the plankck is in equilibrium

Thiss is will happen when the moment due to bucket is balanced by moment due to weight of painter

Or, 67*L = 71*d

Or, 67*1.1 = 71*d

d= 1.038 m

This is the required answer