# Lifting a Beam with a uniform weight distribution

• userAA
In summary, the weight of the beam is distributed differently as it is lifted due to the introduction of horizontal forces, and the weight at the hinge decreases as the beam becomes more vertical.
userAA

## Homework Statement

Hi There,

I'm having trouble understanding (what I guess should be) a simple concept and so I can't apply it to a project I'm working on (also kind of rusty on torques and mechanics problems)

If I have a hinged beam (of uniform weight) and I lift it from one end and stay at rest, am I effectively lifting half the weight of the beam? (Please look at my calculation below). If so, how come when we lift the hood of our car it feels as though we are lifting less weight as the hood moves to a vertical position? Is it because it is rotational motion and I would have to consider some other equations (sorry I feel like I study this every year and forget it in a few days after not using it so I'm still referring to youtube videos for now).

The first two images are the question I have posted above (and my attempt at finding that the downward force being half the weight).

The last image is the mechanism I have to model the forces acting on point 2 that requires me to understand what force would be at the tip of the weight. (just so you can understand how this plays into why I'm trying to understand this). All lengths and angles are assumed to be known at every position.

Based on the mechanism I was also thinking that the reaction force applied from the uniform weight might be perpendicular to it but I couldn't convince myself why it would be.

Any direction would be greatly appreciated

## Homework Equations

Fx and Fy and Torque at equilibrium are equal to 0 (please have a look at my attempt at the solution)

## The Attempt at a Solution

∑Fx=0
Rx=0

∑Fy=0
Ry+Fperson-mg=0

∑T=0
@hinge
0=-mg(L/2)(cosθ)+Fperson(L)(cosθ)
simplifies to

Fperson=mg(0.5)
So force applied is half the weight

Problems on Google have the person applying a force but the vector is always shown to be perpendicular. In my case if you look at image 3 with the mechanism supporting the uniform weight, wouldn't the reaction force between the point it touches be exactly downwards?

Last edited by a moderator:
userAA said:
If so, how come when we lift the hood of our car it feels as though we are lifting less weight as the hood moves to a vertical position?
Many vehicle hoods are "spring loaded" if they have gas charged struts or coiled torsion springs or even long tube coils on old cars it takes weight off of the hood making it feel lighter, unless you try to open it very fast then the mass would take more energy to accelerate and the strut type hoods will resist the sudden motion.

jerromyjon said:
Many vehicle hoods are "spring loaded" if they have gas charged struts or coiled torsion springs or even long tube coils on old cars it takes weight off of the hood making it feel lighter, unless you try to open it very fast then the mass would take more energy to accelerate and the strut type hoods will resist the sudden motion.

My car doesn't have a spring loaded hood but I don't know why I still feel like I'm using less of a force when it's getting to a vertical position :/

But the mechanism I'm trying to break down the torsional forces on (last image) does have a coiled torsion spring! So do you think that the force from the vehicle on gas charged struts/coiled spring mechanisms will always be a reaction vertically downwards? In which case the force of the hood at that point will be 1/2 the weight?

userAA said:
My car doesn't have a spring loaded hood but I don't know why I still feel like I'm using less of a force when it's getting to a vertical position :/
Certainly, it should tend towards 0 at vertical. Most hoods don't open that far...

userAA said:
But the mechanism I'm trying to break down the torsional forces on (last image) does have a coiled torsion spring!
And the contribution from the spring will decrease as it uncoils it's PE.

let's forget about hoods and mechanisms and just look at lifting a beam hinged at one end lying on the floor , and start lifting it (rotating it) by grabbing it at one end and applying a force there. Initially, your force is vertical and equal to half the weight, but as you lift it, there are now forces introduced in the horizontal direction as well, and the weight shifts to the hinged end as you push perpendicular to the beam. Imagine that now the beam is completely vertical, and you can let go of it at the top and all the weight is at the hinge, and in theory the beam is still stable at that point.

## 1. How can the weight distribution of a beam affect its lifting capacity?

The weight distribution of a beam can greatly impact its lifting capacity. A beam with a uniform weight distribution, meaning the weight is evenly distributed along its length, will have a higher lifting capacity compared to a beam with an uneven weight distribution. This is because a uniform distribution allows for more equal distribution of the load, making it easier to lift.

## 2. What is the maximum weight a beam with a uniform weight distribution can lift?

The maximum weight a beam with a uniform weight distribution can lift depends on several factors, such as the material and dimensions of the beam, as well as the strength of the lifting equipment being used. However, generally speaking, a beam with a uniform weight distribution can lift a heavier load compared to a beam with an uneven weight distribution.

## 3. How does the length of the beam affect its lifting capacity?

The length of a beam can greatly impact its lifting capacity. The longer the beam, the more it will flex and bend under the weight of the load. This can decrease its lifting capacity and make it more difficult to handle. It is important to consider the length of the beam when determining its lifting capacity.

## 4. Can the lifting capacity of a beam be increased by adding support?

Yes, the lifting capacity of a beam can be increased by adding support, such as columns or braces, at strategic points along its length. This helps to distribute the weight of the load more evenly and reduces the amount of flex and bending in the beam. However, it is important to ensure that the added support is able to handle the additional load and does not become a point of weakness in the structure.

## 5. What are some safety precautions to consider when lifting a beam with a uniform weight distribution?

When lifting a beam with a uniform weight distribution, it is important to ensure that the lifting equipment being used is appropriate for the weight and dimensions of the beam. It is also crucial to have a clear understanding of the beam's lifting capacity and to never exceed that limit. Additionally, proper safety measures, such as wearing personal protective equipment and having a team of trained individuals assisting with the lift, should always be followed to prevent accidents or injuries.

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