- #1

tyrostoken

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## Homework Statement

Given: A 300 kg walkway supported by two rollers(at points A and B) with center of mass at G.

Find: The tension T in the horizontal cable attached to the cleat at point B and the force under the roller at A.

## Homework Equations

∑M = 0

ΣFx = 0

ΣFy = 0

## The Attempt at a Solution

Free body diagram of the bridge has Normal force vertically upwards with point of application A(Na) , Weight(W) vertically downwards at G, Normal force perpendicular to walkway directed away from water(Nb), and Tension(T) horizontal to the right at point B.

∑Mb = 0 (moment at point B)

0 = +W(4cos30°) - Na(8cos30°)

Na = (W(4cos30°))/(8cos30°)

Na = 1472 N

So far this answer is known to be correct for Na.

ΣFx = 0

0 = T - Nbcos30°

T = Nbcos30°

ΣFy = 0

0 = Na - W + Nbsin30°

Nbsin30° = W - Na

Nb = (W - Na) / sin30°

Plugging in the known values and Na that we solved for yields the incorrect answer. Why can't I add up the components of the force vectors or what am I doing incorrectly?