Why does the force increase when holding a bag at an angle of 45 degrees?

[Physicsterian]

Hi,

If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or provide a source where I can find information on it considering I am just a beginner in the area (I can work with the SOHCAHTOA rule and know how to break gravity force in its X and y component).

 

[russ_watters]

HI,

Welcome to PF!

If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or provide a source where I can find information on it considering I am just a beginner in the area (I can work with the SOHCAHTOA rule and know how to break gravity force in its X and y component).

Bag? As in non-rigid? I don't see how a person can hold a non-rigid bag at a 45 degree angle. As soon as one person let's go of the bag it will swing toward the other person. Maybe it would help if you draw a picture of what you are referring to.

 

[mfb]

If you hold handles of a bag at an angle then you have a horizontal and a vertical component of the force. Only the vertical component contributes to holding the bag up, the horizontal one does not (the two people "pull on each other" indirectly via these forces). A force balance can show how large each component is. Then you can compare it to the case of one person holding the bag with vertical handles.

 

[A.T.]

If 2 people are holding a bag at an angle of 45 degrees each, and then only person is going to hold it, it is being said that the force that will have to be applied by that one person will be 1.5 times greater than when he was applying it together with the other. Can anyone explain this or provide a source where I can find information on it considering I am just a beginner in the area (I can work with the SOHCAHTOA rule and know how to break gravity force in its X and y component).

Forces add as vectors:

More:
https://www.antonine-education.co.uk/Pages/Physics_2/Mechanics/MEC_02/Mechanics_2.htm
https://en.wikipedia.org/wiki/Euclidean_vector#Addition_and_subtraction

 

[Physicsterian]

It helps me to know that I need to focus on the vertical components and thanks a lot for the valuable sources. I threw an eye over it and I am quite sure, it will make me understand the concept.

I assume it is a rigid body, since the complexity of the questions is said to be easy and have a practical character.

It initially feels kinda complex, as not much info is provided; no force and not even the weight of the object is given, only that the force that needs to be applied is 1.5 times greater in situation b. I need to proof why is it 1.5x greater. The approach that seems most wise to me is choosing a random value for the weight, and applying the trigs in the sources from that point on. Do you think my approach sounds proper?

Thanks a lot in advance

 

[mfb]

Here is the weight: $x$. You don't have to pick a numerical value, the weight will cancel in the ratio later.

 

[A.T.]

I need to proof why is it 1.5x greater.

It's actually closer to 1.4, so don't get hung up on the 1.5 approximation.

 

[Physicsterian]

Thanks a lot everybody, for the support.

I indeed eventually arrived at 1,4, good to know, that takes away some doubt :)! The X that I found calculating it the way I did it, is a ratio number and not the weight. Am I doing it mathematically/systematically correct? Or is it maybe better to say delta W = x or formulate it slightly differently?

The websites you sent me are very useful in answering many other questions I was having difficulties with, so that will keep me busy for the coming couple of days.

Thanks again!