To the right is a diagram of a sign hanging from a wall with a boom and a suppor

Question

To the right is a diagram of a sign hanging from a wall with a boom and a support wire. If the boom is uniform in density (its center of mass represented by the black dot) and weighs about the same as the sign, which of the force vectors shown most closely approximates the direction of the total force on the boom by the wall? An axle is balanced on a bar such that a wheel is on one side and a weight is on the other, as in the diagram to the right. The wheel is rotating such that the outer edge facing out of the page is moving upward (clockwise as viewed from the right). If the balance bar is suddenly slid along the axle to the right, which way (if any) will the wheel initially move? up down into the page out of the page it will not move at all

Explanation / Answer

suppose mass of sign board and beam is m.

balancing moment about hinge point

then, (L/2 x mg ) + ( Lx mg) - ( L x Tsin@) = 0

T = 3mg / 2sin@

then horizontal component Fx will be

Fx = Tcos@   = 3mg / 2tan@

in vertical,

Fy - 2mg + Tsin@ = 0

Fy = 2mg - 3mg/2 = mg/2

angle of force = tan^-1( Fy / Fx) = tan^-1 ( tan@/3

so line will be D.

ANs(d)

please post one question in single linlk.

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