What is the vertical force exerted by pier P on the left end of the bridge?

[vorcil]

FORCES On a bridge

A bridge, constructed of 11 beams of equal length L
and negligible mass, supports an object of mass M


as shown. (Intro 1 figure) Real bridges of this sort have steel rockers at the ends (check one out sometime), these assure that the support forces on the bridge are vertical even when it expands or contracts thermally.

Throughout this problem, use g for the magnitude of the acceleration due to gravity.

Find FP , the vertical force that pier P exerts on the left end of the bridge.


My attempt:
I know the mass exerts a clockwise torque on the left end
and that their is also the force of the whole bridge on the bridge due to gravity

so Fp = Torqueduetomass + the whole weight force /2 (because it's halved? due to theother end of the bridge helping out)

 

[Doc Al]

Substituting in (1) for h from (2), I from (3), and w from (4):
(mv^2 + 2mv^2 / 3) = mgs sin(a)

Looks like you dropped a factor of 2.

 

[vorcil]

Looks like you dropped a factor of 2.

wait can you please explain?

(mv^2 + 2mv^2/3) /2 is correct?

 

[Doc Al]

(mv^2 + 2mv^2/3) /2 is correct?

Yes, that is correct. (Don't lose that 2 in the denominator.)

 

[vorcil]

Yes, that is correct. (Don't lose that 2 in the denominator.)

thanks, I've changed the question now this is one I've had ages to do but keep getting it wrong

 

[Doc Al]

thanks, i've changed the question now this is one I've had ages to do but keep getting it wrong

Don't go back and change the question. That turns the thread into gibberish.