Force needed to make a disk climb a step

[Towelie]

[SOLVED] Force needed to make a disk climb a step

Howdy ho. First off, let me say that I'm a newbie here, and I'm not sure if this is the correct place to put this doubt. Here's the deal:

Homework Statement

We have a disk, and we need to know the force F needed to have it climb the step, with 50mm. The force is applied at the top of the disk.

...F <---- ...
......|...|
.....|...|
___________|...|
...50mm | |...|
....|___..._______

Sorry for that draw, it's the best I could do.
The only known data is:
the step has 50mm;
the disk is uniform and weights 40N;
no friction is to be considered.

Homework Equations

-

The Attempt at a Solution

I've tried solving it in several ways. I've considered a normal vertical reaction 1 between the ground and the disk, and considered a normal diagonal reaction 2 between the disk and the tip of the step. I also considered that the angle this reaction 2 makes is 45º. So, I concluded that, in the vertical axis, we have: 40 = N1 + N2.sin45º.
After this, we would have in the horizontal axis the force F and N2.cos45º. I thought that one condition for the disk to climb the step would be: F > N2.cos45º.
However, this wouldn't be enough. So I used the moment. The moment the force F causes in the center of the disk is F.r . We do not know r, so this would lead to another variable in another equation. So, unless there is missing some data here, I don't know how to solve it. I have the solution, and it says the force should be F=17,88N .

Sorry for any language error, english is not my native language, and is not the language I'm using in classes, so I may have mistaken some technical terms.

 

[Doc Al]

Taking moments is the right approach. Hint: You can choose any pivot point you like, so choose wisely.

 

[Towelie]

I can't seem to get a solution. I tried using the tip of the step as the pivot. But the distance between this pivot and the 3 forces (weight, reaction 1 and force F) all depend on R. Besides, the sum of all moments is depending on reaction 1, which is unknown.
Thanks for any help

 

[alphysicist]

Hi Towelie,

Was this a book problem? This answer does depend on R so they would have to give it to you somehow. (The answer you have of F=17.88 N corresponds to a radius of 15 cm.)

 

[Towelie]

No, it's in a work sheet, made by my professor. It is indeed possible some data is missing, it wouldn't be the first time. But thanks for all your help!

 

[Doc Al]

I tried using the tip of the step as the pivot. But the distance between this pivot and the 3 forces (weight, reaction 1 and force F) all depend on R.

You need to be given R.

Besides, the sum of all moments is depending on reaction 1, which is unknown.

At the instant the disk begins to rise up, what is that reaction force?

 

[Towelie]

That would be 0, am I correct?

 

[Doc Al]

That would be 0, am I correct?

You are correct.

 

[Towelie]

Ok. So I assumed the instant the disk is rising up, that is, N1=0. I also assumed R=0,15 , like alphysicist said. In this scenario, all we need is the moment caused by force F to be bigger than the moment caused by weight:

F . 0,25 > 40 . 0,1118 (=) F > 17,888N

The same result from my solutions. So I think it is correct! Thank you very much for your help, Doc Al and alphysicist.