Question

A uniform plank is 8-m long and weighs 99 N. It is balanced on a sawhorse at its center. An additional 182 N weight is now placed on the left end of the plank. To keep the plank balanced, it must be moved what distance (in m) to the right? Round your answer to the nearest tenth.

Answer 1

Answer:

It must be moved by 2.59 m to the right

Explanation:

To keep the plank in uniform state, the moment at sawhorse = 0

Let y be the distance of saw horse from left of plank.

Weight per unit length of plank $=\frac{99}{8}=12.375N/m$

Taking moment about saw horse

Moment due to left portion,

         182 x y + 12.375 x y x 0.5 y = 182 y + 6.1875 y²

Moment due to right portion,

         12.375 x (8-y) x 0.5 (8-y) = 396 + 6.1875 y² - 99y

So to keep balance these moments should be same

         182 y + 6.1875 y² = 396 + 6.1875 y² - 99y

         281 y = 396

                y = 1.41 m

Distance moved to right = 0.5 x 8 - 1.41 = 2.59 m

So it must be moved by 2.59 m to the right