The force required to raise a bridge/lever to an angle?

[helppls]

Homework Statement

Tower bridge in London is an example of a bascule bridge (moveable bridge) where each part that is raised up is called a ‘span’. In this photo, the two spans are raised to an angle of 38° to let two tug boats through. Each span is 30.5 m long and weighs 1 x 108 kg (you can assume that the mass is distributed evenly).
a) Calculate the force required to raise one span to an angle of 38°
b) How does this force change if a span is raised to an angle of 85°?

I know that the center of gravity is at 15.25 m , which should then be the distance R
the bridge weighs 9.8*10^8 N

Homework Equations

torque = r*F
torque = r*F*sin(theta)

The Attempt at a Solution

a) the torque, I think, is
15.25 * (9.8 x 10^8) *sin(38) = 9.2 x 10^9 Nm ... but I don't know how to find the force required?
b) I am assuming that the force required lessens as you increase the angle of the bridge. I'm stuck.

 

[Orodruin]

In this photo

What photo? You did not provide it.

 

[helppls]

sorry, yeah, it's just a photo of the bridge

 

[haruspex]

Calculate the force required to raise one span to an angle of 38°

There are two troubling aspects to that wording.
First, as you appear to have realized, it does not require any particular force; what it does require is torque.
Secondly, does it really want the torque to raise it to that angle or the torque to hold it at that position? You have attempted to answer the second. However, check your trig choice.

 

[helppls]

Thanks for your response,
should I use cosine to make the force acting perpendicular to r?
If I'm just calculating the torque to hold it in position, how do I calculate the torque required to raise it to that position? Wouldn't that be variable?

I've been struggling with the wording on this assignment :(

 

[haruspex]

should I use cosine to make the force acting perpendicular to r?

You need the perpendicular distance ("moment arm") from the pivot to the line of action of the load force.

how do I calculate the torque required to raise it to that position? Wouldn't that be variable?

Yes, but it has a maximum. To raise it you need to achieve that maximum torque.

 

[helppls]

You need the perpendicular distance ("moment arm") from the pivot to the line of action of the load force.

Yes, but it has a maximum. To raise it you need to achieve that maximum torque.

Thank you! This makes sense. So I need to calculate the torque when the arm is level as this would have the maximum horizontal distance from the pivot arm and thus the maximum torque.

 

[haruspex]

Thank you! This makes sense. So I need to calculate the torque when the arm is level as this would have the maximum horizontal distance from the pivot arm and thus the maximum torque.

Yes.