Static Friction, Kinetic Friction and Rolling Resistance query.

[mart7x]

Hypothetically, if I had a sphere and a block (of the same mass and material (hence the same coefficients of static friction for both interfaces) both stationary on a surface, they would require the same force to initiate motion?

Once moving, a coefficient of sliding friction is employed in the case of the block, and a coefficient of rolling resistance in the case of the sphere, hence the sphere requires a much lower force to maintain motion (assuming the coefficient for rolling resistance is lower)?

Are these questions true or false? I have had a few debates with lecturers and although this may be a very straightforward questions (very simple mechanics) I am curious to hear others opinions.

Thank you,
Martin

 

[tiny-tim]

Hi Martin!

Hypothetically, if I had a sphere and a block (of the same mass and material (hence the same coefficients of static friction for both interfaces) both stationary on a surface, they would require the same force to initiate motion?

A rolling body is not impeded by static friction.

Static friction does not resist rolling (technically, it helps it).

A very small force should still make the sphere roll.

Only if the force is less than the rolling resistance (basically, the very slight tendency of the wheel to deform where it meets the ground) will the wheel fail to roll.

 

[mart7x]

Ok thanks tiny-tim, is it then just mass of the sphere that is resisting motion? I have a slab resting on a few spheres and I am experimentally testing the force required to move it, but I would like to first model the problem analytically. How then do I go about finding the force required to move a stationary sphere? Do I simply have to assume an acceleration I wish to achieve and multiply by the objects mass (F=ma)?

Thanks again

 

[tiny-tim]

hi mart7x1!

Ok thanks tiny-tim, is it then just mass of the sphere that is resisting motion?

basically, yes

… How then do I go about finding the force required to move a stationary sphere? Do I simply have to assume an acceleration I wish to achieve and multiply by the objects mass (F=ma)?

yes, except that instead of the mass (m), you must use m + m_r, where m_r is the "rolling mass", I/r²

(but the weight, mg stays the same, in equations like mgsinθ = ma)

for example, for a cylinder rolling down a plane, you use mgsinθ = 3ma/2, and for a sphere (as in Newton's famous experiment), you use mgsinθ = 7ma/5

(technically, the mass of a car should be increased by the very small 4I/r², for the four wheels)

 

[mart7x]

Ok brilliant, but I don't use the rolling mass for a stationary object (not yet rolling), right? And could I possibly find the force to move the sphere if I didn't know the acceleration- essentially the critical force that I would need to apply to initiate rolling? Thanks for all the help!

 

[tiny-tim]

… could I possibly find the force to move the sphere if I didn't know the acceleration- essentially the critical force that I would need to apply to initiate rolling?

if we ignore rolling resistance, there's no minimum force to initiate rolling

 

[mart7x]

Sorry forgive me if I'm repeating what has been mentioned, but to clarify rolling resistance IS applicable to a stationary object (that could potentially roll)?

I have a stationary sphere of mass = 10kg, Coefficient of Rolling Resistance = 0.05.

The force required to start the ball rolling:

F = mg

F = 10 * 9.81 =98.1N

F = Normal

Fresistive = Crr*N

Fresistive = 0.05 * 98.1

Fresistive = 4.905 N

Force required to make the sphere roll > 4.905 N

 

[tiny-tim]

Sorry forgive me if I'm repeating what has been mentioned, but to clarify rolling resistance IS applicable to a stationary object (that could potentially roll)?

yes (both stationary and moving), but I've never seen an exam question that doesn't intend you to ignore rolling resistance (in the same way that we ignore air resistance etc)

except this one …

I have a stationary sphere of mass = 10kg, Coefficient of Rolling Resistance = 0.05.

The force required to start the ball rolling:

F = mg

F = 10 * 9.81 =98.1N

F = Normal

Fresistive = Crr*N

Fresistive = 0.05 * 98.1

Fresistive = 4.905 N

Force required to make the sphere roll > 4.905 N

yes, that's correct

 

[mart7x]

Thank you very much I have been struggling for a long time to set this record straight! To put this into context, I am creating an experiment within the lab which is testing the horizontal force to move large monument stones (such as Stonehenge in Britain) when resting on rollers/carved ball bearings. I am loading up a vertical force of up to 40 tons and observing the relationship to the horizontal force required to initiate rolling. I was keen to model this analytically before conducting this experiment and it was this concept of stationary objects that would potentially roll that threw me for a while (this is why I didn't want to ignore rolling resistance). Once again, thank you for your time!

Martin

 

[tiny-tim]

Hi Martin!

To put this into context, I am creating an experiment within the lab which is testing the horizontal force to move large monument stones (such as Stonehenge in Britain) when resting on rollers/carved ball bearings.

The major problem was the unevenness of the ground … this probably far outweighed rolling resistance of the rollers …

how are you going to model that in the lab? ​

 

[mart7x]

AHH well it is a slightly unique (maybe controversial!) theory that I have been hired not only to validate but to critique-

To put it as simply as possible: hundreds of carved granite spheres have been found around monuments such as stonehenge with deviations in diameter of less than 2mm (I know that seems crazy for the engineering capabilities of Neolithic man!). Now this coincidence suggest that these were designed to be used in unison (possibly to transmit load) rather than individual tools. Now as oak was such an abundant material at the time, and as they were more than capable of carving accurate spheres, the theory suggests that they could have carved grooves along lengths of oak, filled these with the carved spheres, and lain a reciprocating rail on top. Two of these mechanisms parallel next to each other with a stone on top becomes a fairly efficient method of transporting heavy objects. This may all seem far-fetched but that's why I'm here asking questions!

You may find this very boring but there is a documentary about it online with a small segment dedicated to this idea if your interested (6:00 on this link): http://www.youtube.com/watch?v=VxMLJegGQEI&feature=relmfu

 

[Maertens]

yes (both stationary and moving), but I've never seen an exam question that doesn't intend you to ignore rolling resistance (in the same way that we ignore air resistance etc)

except this one …


yes, that's correct

I have here some questions.
1: In the formula you don't count with the radius of the wheel. So if you have a big wheel, small wheel with some kind of width it is the same force you need to let the wheel roll??
2: How do you know the coefficient? In my case I use a cast iron wheel diameter 140mm x 40mm with included tread of PU shore hardness 92A - 2cm thickness.
3: Is there a formula to know the pressure the wheel has on the floor? Because I need to know what wheight I maximum can load to have a pressure on the floor of 10kg/cm²...

Thanks,