Calculating the force required to move a golf ball up a ramp

[tnjake]

Homework Statement

Hello and good day,
I am currently working on a design project which involves creating a golf ball collecting machine. The current design method involves the golf ball being swept up a ramp by rotating sweeping arms. I am trying to calculate the force required to push the ball up the ramp. The only forces acting on the ball while it is on the ramp that I can think of are the forces due to gravity and friction.

mass of a Golf ball = 45.93 grams

Homework Equations

The force to push the ball up the ramp as I understand it would be
https://www.physicsforums.com/file:///C:/Users/jacob/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png
Fpush = mgsin(theta)
Friction force is equal to
https://www.physicsforums.com/file:///C:/Users/jacob/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png
Ff=μsFn
Normal force Fn is equal to
https://www.physicsforums.com/file:///C:/Users/jacob/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png
Fn=mgcos(theta)
Therefore, Friction force is equal to
https://www.physicsforums.com/file:///C:/Users/jacob/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png
Ff=μsmgcos(theta)
Therefore, Fpush is finally equal to
https://www.physicsforums.com/file:///C:/Users/jacob/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png
Fpush=mgsin(theta)+μsmgcos(theta)
3. The Attempt at a Solution
If these are the correct equations for this situation, and the angle of theta = 20°
Then the force to push the golf ball is equal to
Fpush=(45.93)g(9.81)m/s^2*sin(20)+μs(45.93)g(9.81)m/s^2cos(20)
https://www.physicsforums.com/file:///C:/Users/jacob/AppData/Local/Temp/msohtmlclip1/01/clip_image002.png

The only problem with this is that because I am at an early stage in the design process, no material has been chosen for ramp construction. Therefore, I don't know what the coefficient of friction would be. A classmate of mine said that I could instead, use the moment of inertia for a sphere and I could neglect the friction. I am slightly puzzled about going about it that away though.

 

[Merlin3189]

Hello and welcome to PF

Your images have not shown up (to me at least). You may need to save on your computer as: png, jpg, jpeg, jpe, gif, Max width: 960 pix, Max height: 720 pix (Also accepted file types: zip, txt, pdf, docx, xlsx but I don't know if they display?) then use the upload button at the bottom and insert into your post.

Some initial thoughts;

A sketch (or more) of your design would be useful.

Moment of inertia won't avoid the need to consider friction, because;
The ball is going to slide (rather than / as well as) roll, as it is in contact with two surfaces .
Moment of inertia (and linear inertia) will be less significant than weight and friction, if the ball is moved slowly. Though you may have to take these accelerations into account if you want to zip it up the ramp quickly.

Depending on the way your mechanism works, you may be pushing horizontally or parallel to the ramp and you may not be pushing perpendicular to the motion in the horizontal plane.

I haven't checked your calculations, but it looks as if you have the right sort of ideas (it's not worth checking until I see your diagrams.) But I would say that at this stage there is no need to use 3 or 4 sf. There are still a lot of uncertainties ( eg. friction, degree os sliding/rolling) so make life easy and get some ball park figures to maybe 2sf (and even just 1sf sometimes) to get a feel for the size of the issues. If μ turns out to be between 0.1 and 0.2 say, where does a mass to 4sf get you? When you have more data, do a more precise calculation and estimate the error margin or range of possible values.

Be a bit wary of coefficients of friction and the Coulomb model in the context of plastics. But it's all you've got and at light loads with smooth surfaces, it should be good enough. You could do a few experiments* with whatever materials you have to hand. You may (?) find some useful values on the web. I think eventually you'll have to determine friction by experiment, using the materials and conditions of your prototypes.
*Incidentally, if I were marking a project like this, I'd be very interested in how people did research like this. Irrespective of the quality of the final solution, I'd be giving credit for these parts of the project.

Good luck with your project.