# Problem: If P = 500 lb and L = 12 ft., what are the magnitudes of w1, w2 ?

###### FREE Expert Solution

Relabel the figure as:

From the equilibrium condition:

$\overline{){\mathbf{\Sigma }}{\mathbf{F}}{\mathbf{=}}{\mathbf{0}}}$

The vertical equilibrium:

The varying load given is divided into a rectangle and a triangular load.

We have:

w1L + (1/2)(w2 - w1)L = P + 2P

w1L + (1/2)w2L - (1/2)w1L = 3P

(1/2)w1 + (1/2)w2L = 3P/L

w1 + w2 = 6P/L

Considering the moment at B:

w1L + (1/2)L + (1/2)(w2 - w1)L + (1/3)L = P(2/3)L + 2P(1/3)L

w1L2/2 + w2L2/6 - w1L2/6 = 4PL/3

2w1 + w2 = 8P/L

###### Problem Details

If P = 500 lb and L = 12 ft., what are the magnitudes of w1, w2 ?

What scientific concept do you need to know in order to solve this problem?

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