friction and rolling resistance, and work done queries

tiny-tim

yes
not following you

at constant speed, there is no turning force from the engine (i'm assuming we're ignoring air resistance etc)
if the net force is zero, the speed stays whatever it was in the first place

sgstudent

Like when I pull that trapdoor the net moment is 0 but there is constant speed while when a ruler is place on a pivot and two objects resting on both sides and moment is 0 it there is no movement of the plank even though in both cases net moment is 0 so how do I tell if an plane will move with constant speed or 0 speed at all. Thanks for the help!

tiny-tim

it depends what the angular speed was just before the net moment was zero

for the trap door, you had to get it moving at that angular speed by using a slightly greater applied moment, and then when you reckoned that the angular speed was just right, you reduced the applied moment so that the net moment was zero

sgstudent

Oh so it depends on the angular speed before I reduce the moment to 0 does it work the same as for forces. Like if I apply a force then when I stop applying force (assuming no friction or retarding force) then it will stay at that speed forever? Thanks for the help!

tiny-tim

that's absolutely correct

also, if you apply a force to a body that is impeded by friction, then if you stop increasing the force when it balances the friction force, it will stay at that speed forever

sgstudent

Hi tiny tim! After discussing this with my friend using our O level knowledge, we came to a conclusion. But we have some queries.

So firstly, we have our driving wheel on the air and the engine is turned on. So the Free Body Diagram would look like this: http://imgur.com/xVk0w

So in this case the net force of the wheel is 0N as F2 and F1 are equal in magnitude. However, about F1, there is a net moment which turns clockwise (F1XL).

Then now we put it on the ground and and experiences a friction oppsoing F1 as friction opposes force in a single plane of contact. So now, the Free Body Diagram would look like this: http://imgur.com/Pw1oh

From this, since F2-F1=0N, so the net force=friction only. While the wheel still has to maintain its clockwise moment so F1L > FrictionL and since L is a constant, so F1>Friction.
So from here, it all makes sense to us, but then after thinking again since that friction force that we have been dealing up to now is static friction so shouldn't F1 be equal to friction? But if F1 is equal to the friction, the the wheel would not be able to turn in the first place.

So we were stuck at this part with no solution in mind. Could you help us out with this? Thanks 7

tiny-tim

hi sgstudent!
first, can i check that we mean the same thing by "driving wheel"?

a driving wheel is one that is forced to turn by a torque from another part of the vehicle

a non-driving wheel is one that simply receives a (linear) force from another part of the vehicle, or another vehicle (or animal)

so we normally draw the free body diagram of a non-driving wheel with a straight arrow, usually from the centre of the wheel, representing the force

while we draw the free body diagram of a driving wheel with a small circular arrow (anywhere), representing the torque

alternatively, we can represent that torque by two equal and opposite straight arrows, but although i agree we could place them anywhere, it would be normal to place them equal distances above and below the centre of the wheel …

your arrow at the bottom of the wheel may be confusing you, since the bottom of the wheel has no significance

of course, as shown, the centre of the wheel will stay where it is, but the wheel's rotation will accelerate

again, the position of F₁ at the bottom of the wheel has no significance, it could be anywhere (so long as FL equals the torque)

in this case, the wheel's rotation will accelerate slower than before (because the friction is an opposing torque about the centre of mass), but the centre of the wheel will (linearly) accelerate

i did the calculation for a non-driving wheel in post #14

do the calculation for this driving wheel, and you should see that there is no difficulty

i don't understand why you say "since that friction force that we have been dealing up to now is static friction so shouldn't F1 be equal to friction?"

static friction is not µN, or any other formula, it is simply the horizontal component of the total reaction force at the surface …

and the reaction force is always calculated (even in non-rotational cases, such as a static ladder) as the "missing" force that has to be inserted to make the equation (between the known forces and the geometric constraint of the surface) balance …

so the static friction can be anything between 0 and µN

sgstudent

Hi Tiny Tim, it has been a while!

Yup, we have the same defination of the wheel whereby the force is actually turning it. But again for the engine i was thinking the force turing it looks like this: http://imgur.com/8doMX
whereby the engine has an axle to push against to turn it. So in air/ice one force (by the engine) would be at the wheel's end and one at the centre of the wheel (equal in magnitude) which prevents it from moving forward? So it is something like this: http://imgur.com/h4wg3 I think this picture would work even if its not a car as wheelchairs use the same pinciples where the person sitting would push the wheel for it to turn.

So after googling about this topic for a long while i came across a old post by you haha. This was what you said: A car moves forward because the engine forces the back axle to turn.

If the car was on ice, the back wheels would spin, but the rest of the car would be still.

The torque from the engine causes a force at the bit of the tyre in contact with the road. So long as that force does not exceed the maximum static friction, that force will equal the actual friction force, and the bit of the tyre in contact with the road will not move.

(Newton's first law on that bit of the tyre: zero total force means zero change in movement.)

The car will move, because the only external horizontal force on it is the actual friction force.

So i understand now that the F engine=Static friction (without slipping though). But if F engine=Static friction, the won't the net moment be 0Nm and as a result, the wheel should not even be able to start turning (if we consider the wheel to be at rest initially). Even if the wheel has a net force which is the friction (http://imgur.com/uMQjk).

So I don't understand how the wheel can rotate. The car and wheel experiences a net force but no net moment. So I'm pretty confused about this.

Also, another thing that I'm confused is that in the wheelchair/driving wheel example, the wheelchair bound person would push the wheel only at the top, so would that mean the static friction at the bottom would have the same magnitude (http://imgur.com/Kafh6)? What allows this phenomenon to happen since the force is not at the same point of each other?

Thanks Tiny Tim, you rock!

tiny-tim

no, even at zero acceleration, you also have to include the reaction force from the load

in all cases, the equations come from two free body diagrams: one for the wheel, and one for the load (or for the wheel-and-load combined) …

in particular, the first one will include the reaction force between the wheel and the load …

i think it's your failure to include that that is confusing you

try writing out the actual equations, one for the wheel and one for the person (including the reaction force between them in each), and using the same linear acceleration for both …

what do you get?

sgstudent

Hi tiny tim because we haven't learned any theory on this so we don't really know any equations besides F=ma and moment=Fd.. Also, what was that reaction force you mentioned? Thanks!

tiny-tim

the only other equations you need are τ = Iα (total moment of force = moment of inertia times angular acceleration), and the "rolling constraint" v = ωr, a = αr …

just do F = ma for the person, and τ = Iα for the wheel (about the centre of the wheel), remembering to include the reaction force ±R in both (it'll be + for one and - for the other)

the reaction force is the "internal" (linear) force between the axle-and-wheels and the body of the wheelchair …

it's what pulls the body! …

for each part separately, it's an external force, of course

(technically, there's also a reaction torque, from the friction between the axle and the body)

sgstudent

Hi Tiny Tim, are there any pictures because i can't virtualise that. I was thinking the forces should look like this: http://imgur.com/WNSV7

Firstly, will my F friction = F push? Because of static friction.

So using the formula, the net F=F friction for the wheel but for the person on the seat the net F= 0?

As for moment of the wheel, it is 0Nm?

I'm getting realise confused about this now. Is there a explanation for this concept? Because I'm really curious about this haha. Thanks

tiny-tim

hi sgstudent!

i'm sorry for the delay
first, it's a lot better if you stop using "F" for all your forces: use eg P for push, F for friction, R for reaction etc

for the free body diagram of the person, there's two horizontal forces …

(i'm ignoring all vertical forces)

… the push force (same as the reaction force) from the wheel onto the person's arm, and the friction force from the seat

together, they make the mass of the person times acceleration

for the free body diagram of the wheelchair, there's three horizontal forces …

… the push force (same as the reaction force) from the person's arm onto the wheel, the friction force from the person onto the seat, and the friction force from the ground

together, they make the mass of the wheelchair times acceleration

of course, you can also do a free body diagram for the wheel on it own, or for the person and the chair combined (excluding the wheel), or for the person the chair and the wheel all combined

(for the wheel on its own, there's also a small friction torque from the axle of the wheel onto the wheel)
there's only two forces, so F_push - F_friction = ma (which is 0 only if a = 0)
if a = 0, yes
if α = 0, yes (otherwise, it's Iα)

sgstudent

Hi Tiny Tim

But i thought the Fpush must always be equal to Ffriction as the Ffriction is static friction. So does it mean that the torque of the wheel will be just the friction from the person to the seat? Thanks

tiny-tim

if the rider is accelerating, then the friction force from the seat must be more than the force on his arm from the wheel, mustn't it?

sgstudent

But how is that possible? Isn't the push force equal to the static friction?

tiny-tim

which static friction?

the push force from his arm on the wheel equals the static friction force on the top of the wheel (it's just another name for it)

but that doesn't equal either of the other two friction forces (on the seat, and on the ground) unless the acceleration is zero