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

• helppls
If you use torque = force x moment arm, the moment arm is the distance from the pivot to the line of action of the force. For a force acting perpendicular to the arm, this is just the length of the arm. But as the force angle decreases, the moment arm increases.In summary, the Tower Bridge in London is a bascule bridge with two spans that can be raised to let boats pass through. Each span is 30.5 m long and weighs 1 x 10^8 kg. To calculate the force required to raise one span to an angle of 38°, the torque must be calculated using the formula torque = r x F x sin(theta). The perpendicular distance from the pivot to
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.

helppls said:
In this photo
What photo? You did not provide it.

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

helppls said:
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.

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 :(

helppls said:
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.
helppls said:
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.

haruspex said:
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.

helppls said:
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.

## 1. How is the force required to raise a bridge or lever calculated?

The force required to raise a bridge or lever to a certain angle is calculated using the principle of moments. This takes into account the weight of the bridge or lever, the distance from the pivot point, and the desired angle. A simple equation, F = Wd, can be used to calculate the force needed, where F is the force, W is the weight, and d is the distance from the pivot.

## 2. Does the length of the bridge or lever affect the force required?

Yes, the length of the bridge or lever does affect the force required. As the length increases, the force needed to raise it to a certain angle also increases. This is because a longer bridge or lever has a greater moment arm, meaning the distance from the pivot point to the weight is longer, requiring more force to overcome.

## 3. How does the weight of the bridge or lever impact the force needed to raise it?

The weight of the bridge or lever is a crucial factor in determining the force required to raise it. The heavier the weight, the more force is needed to lift it to a certain angle. This is because the weight adds to the overall mass that needs to be lifted, increasing the force needed to overcome gravity.

## 4. Does the angle at which the bridge or lever is raised affect the force required?

Yes, the angle at which the bridge or lever is raised does impact the force needed. As the angle increases, the force required also increases. This is because as the angle increases, the weight of the bridge or lever becomes more perpendicular to the direction of the force, making it more difficult to lift.

## 5. Is the force required to raise a bridge or lever constant?

No, the force required to raise a bridge or lever is not constant. It varies depending on factors such as the weight and length of the bridge or lever, as well as the angle at which it is raised. In addition, friction and other external forces may also impact the force needed. It is important to carefully calculate and adjust the force needed to safely and effectively raise a bridge or lever to a desired angle.

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