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annanause

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## Homework Statement

A uniform plank, of weight 30N and length 3m, resting on two supports. The supports are 0.5m and 2.0m from the left-hand end of the plank. A weight of 18N is suspended from the left-hand end of the plank.

By how much should the weight on the left-hand en be increased so that the reaction Y becomes zero?

By how much should the weight on the left-hand en be increased so that the reaction Y becomes zero?

## Homework Equations

The reactions that have been calculated from the first part of the assignment are 107N for point X and 196N for point Y .

## The Attempt at a Solution

Calculations from part a) of the question, which was about finding the reactions at X and Y:

X x 1 = Y x 0.5

mg = 30N x 9.8m/s

X = mg - Y

(mg - Y) x 1 = Y x 0.5

1 x mg - 1 x Y = 0.5 x Y

1 x mg = 1.5 x Y

1 x mg / 1.5 = 1 x 30 x 9.8 / 1.5 = 196N

X + Y = X + 196N = mg

X = mg - 196 = 30 x 9.8 - 196 = 98N

98 + (18 x 0.5) = 107N

X = 107N

Y = 196N

How do I rearrange the calculations from calculating the reactions into finding how much weight that needs to be added? I am pretty sure I need to consider the length (d) of the plank - I can't simply just add 89N to make the 107N into 196N, right?

If there is a general formula/calculation for this, that would be very helpful.

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