Microsoft Interview Question

[Goosemaster]

Originally posted by: Indolent

Originally posted by: Goosemaster

Originally posted by: Indolent

Originally posted by: Goosemaster
1. Because of the infinite static friction, there is no slippage. The force of static friction points backwards, as it is not letting the wheel slide forwards.
2. The x component of force P would be much greater than its y component. The y component is what allows it to go forward without sliding.
3. The opposite and equal (somewhat equal) force has yet to be accounted for, as both P and F are in the backward direction.
4. The Torque of P is directed in the counterclockwise direction.
5. It stays put .


EDIT:

6. I would LIKE TO SAY that with an increased P, it would roll backwards, but I cannot get myself to say it even tough I want to because I can't prove it.

Let's say that it was directly behind the spoke all the way at the rim. In the case the torque would be directed at the center of the circle, which would mean that it would be serving as a torque around the point where the rim is making contact with the pavement. if enough force P was applied, i guess the y component would be great enough to move it backwards without slipping, but it would take a lot of force...

I'm not really understanding what you are trying to say, but your first point is wrong. The force of static friction points forward. I think you are assuming the wheel is rotating about it's axis when it is really rotating about the ground.

Isn't it both?

The force of static friction prevents it from slipping backward, and then foward, which changes the overal axis of rotation....?

I just didn;t point of the last one because I don;t know enough about it

I'm not sure where you are seeing a force that is trying to make the wheel slip forward. Since there is only one point of rotation and one force pulling the wheel, there is only one friction force at the contact point.

Maybe you can help me out of my confusion then.

Without friction, the wheel would rotate in a counterclockwise direction. Static friction, given in the problem, will not allow that to happen in thisdirection.

So given enough of a force P, it would have to face the static friction of sliding in the clockwise direction. Static friction, again, will not allow that to happen in this direction.

This creates a point where by static friction prevents it from slipping in either direction, and once the torque is high enough, it will rotate about htat point....


Basically, can you help me with the logic..?

 

[whattaguy]

I think it will go forward.
My reasoning is this from what I see.

If it were just a force "P", the bike would move backwards since the wheel would turn clockwise because there is no slippage. But because the force is exerted by the string, it cannot magically get longer to allow the wheel to move clockwise. The wheel will move counter-clockwise and move the bike forward half the distance of the arc created by the string.

Sorry, I haven't taken a math or engineering class in a long time...so forgive my poor explanation.

 

[Indolent]

Originally posted by: Goosemaster

Originally posted by: Indolent

Originally posted by: Goosemaster

Originally posted by: Indolent

Originally posted by: Goosemaster
1. Because of the infinite static friction, there is no slippage. The force of static friction points backwards, as it is not letting the wheel slide forwards.
2. The x component of force P would be much greater than its y component. The y component is what allows it to go forward without sliding.
3. The opposite and equal (somewhat equal) force has yet to be accounted for, as both P and F are in the backward direction.
4. The Torque of P is directed in the counterclockwise direction.
5. It stays put .


EDIT:

6. I would LIKE TO SAY that with an increased P, it would roll backwards, but I cannot get myself to say it even tough I want to because I can't prove it.

Let's say that it was directly behind the spoke all the way at the rim. In the case the torque would be directed at the center of the circle, which would mean that it would be serving as a torque around the point where the rim is making contact with the pavement. if enough force P was applied, i guess the y component would be great enough to move it backwards without slipping, but it would take a lot of force...

I'm not really understanding what you are trying to say, but your first point is wrong. The force of static friction points forward. I think you are assuming the wheel is rotating about it's axis when it is really rotating about the ground.

Isn't it both?

The force of static friction prevents it from slipping backward, and then foward, which changes the overal axis of rotation....?

I just didn;t point of the last one because I don;t know enough about it

I'm not sure where you are seeing a force that is trying to make the wheel slip forward. Since there is only one point of rotation and one force pulling the wheel, there is only one friction force at the contact point.

Maybe you can help me out of my confusion then.

Without friction, the wheel would rotate in a counterclockwise direction. Static friction, given in the problem, will not allow that to happen in thisdirection.

So given enough of a force P, it would have to face the static friction of sliding in the clockwise direction. Static friction, again, will not allow that to happen in this direction.

This creates a point where by static friction prevents it from slipping in either direction, and once the torque is high enough, it will rotate about htat point....


Basically, can you help me with the logic..?

hrm, I can try. It is that bolded part that seems to be messing you up. I'm getting confused by it too by the way you are putting it. Your first statement is correct. Static friction prevents the wheel from moving counterclockwise.

I'm just trying to figure out how to explain that second part. The only thing I can think of is that it is not the wheel that is trying to drive the bike, it is the force, P. If the rear wheel was trying to drive the bike backwards, then there would be a friction force pushing to the right at the contact point on the ground.

Even when I'm reading this it is confusing. I just can't think of how to put it. Did this help at all?

 

[GoingUp]

id say fowards...

I also had an interview on site with M$ for their PM position and they didnt ask me a single riddle.

 

[Indolent]

Originally posted by: whattaguy
I think it will go forward.
My reasoning is this from what I see.

If it were just a force "P", the bike would move backwards since the wheel would turn clockwise because there is no slippage. But because the force is exerted by the string, it cannot magically get longer to allow the wheel to move clockwise. The wheel will move counter-clockwise and move the bike forward half the distance of the arc created by the string.

Sorry, I haven't taken a math or engineering class in a long time...so forgive my poor explanation.

The string would not get longer, the wheel would roll up onto the string. Another example of this is with a spool of thread. If you pulled in a similar manner with the thread coming from underneeth, the spool would just wind back up on the string.

 

[ucdbiendog]

Originally posted by: Yossarian
force P isn't important, the moment exerted about the axle by force P is what matters. resolve force P into components parallel and perpendicular to the wheel at the point of contact. the parallel component goes down and to the right, exerting a counter clockwise moment. the bike goes forward.

That is completely wrong. By taking the moment about the axle, you have to consider the non-slip friction force the ground exerts on the wheel. Take the moment about the contact point with the ground. Since there are no forces to be considered besides P, this results in a clockwise moment on the wheel causing it to go backward.

 

[Yax]

Rather than having a nerd debate, did anyone here bother to actually try the experiment?

I mean, you could have someone hold on to the handlebar just to keep the bike up straight, then pull.

EDIT: btw, all those arguing that the bike goes backwards, can you please draw out your argument so I can visualize what you're trying to say? Your words alone just didn't convince me.

 

[ActuaryTm]

Originally posted by: Yax
Rather than having a nerd debate, did anyone here bother to actually try the experiment?

I mean, you could have someone hold on to the handlebar just to keep the bike up straight, then pull.

EDIT: btw, all those arguing that the bike goes backwards, can you please draw out your argument so I can visualize what you're trying to say? Your words alone just didn't convince me.

From a previous reply:

Originally posted by: ActuaryTm

Originally posted by: Kev
I just did a mini experiment with a bottle cap ...

For those wishing to experiment to some degree of accuracy, the top of a CD/DVD media cakebox would work rather well I imagine.

 

[Indolent]

Originally posted by: Yax
Rather than having a nerd debate, did anyone here bother to actually try the experiment?

I mean, you could have someone hold on to the handlebar just to keep the bike up straight, then pull.

EDIT: btw, all those arguing that the bike goes backwards, can you please draw out your argument so I can visualize what you're trying to say? Your words alone just didn't convince me.

I sort of drew a picture. I just don't know how to explain it any better. This is not a debate, it will definietely go backwards. Experimenting would be a good way to prove it to yourself if you have to. If you don't have a friend and a bike, the same principle can be applied to a spool of thread. Just do it on a rubber or grippy surface so it does not slip and have the thread being pulled from underneeth the spool. If that makes sense at all.

 

[Yax]

I did it!!!

Result: It moves backwards.


For those who don't understand, think of it this way:

1. Push or pull in direction P is the same effect.
2. Instead of the bike wheel, think of a giant cylinder or can.
3. Think of yourself standing besides the can and pushing it at the point where the string would have been tied at. You'd be pushing in the direction P.

Now, if you did that, do you think the giant can would roll over you? If it rolls over you, then the bike would move forward. But really, the can will roll towards the direction you're pushing at. (Note: if you're not strong enough to push the can and make it move, just get some friends to help you push and figure out if the can will roll over you when you're all pushing). Its the non-slipping that makes the can roll the other way.

 

[yhelothar]

Originally posted by: Indolent

Originally posted by: RagingBITCH

Originally posted by: Indolent

Originally posted by: RagingBITCH
I'm still confused as to why it moves backwards. Anyone have a non-technical answer for it? Does the angle you're tugging on the string at make a difference? IE, if the point at which you're holding & tugging the string at parallel to the point to where it's attached, or if you're holding it at seat level for example.

If you were pulling the string so that it was angled down below the point of contact, it would move forward.

Not sure if I explained this very well. I'll see if I can draw a picture

After reading your TuxDave explanation, I got it. A lot of it also depends on where the spoke is, correct? IE, if it was perpendicular to the ground it would have to move forward?

I'm not sure I understand what you mean by where the spoke is.

Here is a picture with the same idea. P1 makes it go right (backward). P2 makes it go left (forward).


*edit* oops, here

That picture doesn't work. The center of rotation is in the center of the wheel.
I just tried this experiment with a cd spindle cover. I taped a USB cable onto it and tugged on it. The cd spindle turned CCW.
Not sure if the wheel would roll forwards if there was infinite friction meaning no slippage. But it's confirmed that the wheel will spin CCW given that force P was applied.

 

[yhelothar]

Originally posted by: Yax
I did it!!!

Result: It moves backwards.


For those who don't understand, think of it this way:

1. Push or pull in direction P is the same effect.
2. Instead of the bike wheel, think of a giant cylinder or can.
3. Think of yourself standing besides the can and pushing it at the point where the string would have been tied at. You'd be pushing in the direction P.

Now, if you did that, do you think the giant can would roll over you? If it rolls over you, then the bike would move forward. But really, the can will roll towards the direction you're pushing at. (Note: if you're not strong enough to push the can and make it move, just get some friends to help you push and figure out if the can will roll over you when you're all pushing). Its the non-slipping that makes the can roll the other way.

Pushing with your fingers is completely different than having a string on there and pulling it.
Your fingers will be pushing up when it hits a \ surface. This will cause it to turn CW, and roll backwards.

 

[MAME]

forward

 

[Goosemaster]

I tried it with my bike and although I wasn't able to secure a "string" perfectly at that point, it did indeed, roll backward....

 

[mzkhadir]

shouldn't it move backward then forward like the force that is applied

 

[Zee]

it has to be backwards. The wheel will roll towards the point of least resistance which is clockwise

 

[ragazzo]

moves forward

 

[Indolent]

Originally posted by: virtualgames0

Originally posted by: Indolent

Originally posted by: RagingBITCH

Originally posted by: Indolent

Originally posted by: RagingBITCH
I'm still confused as to why it moves backwards. Anyone have a non-technical answer for it? Does the angle you're tugging on the string at make a difference? IE, if the point at which you're holding & tugging the string at parallel to the point to where it's attached, or if you're holding it at seat level for example.

If you were pulling the string so that it was angled down below the point of contact, it would move forward.

Not sure if I explained this very well. I'll see if I can draw a picture

After reading your TuxDave explanation, I got it. A lot of it also depends on where the spoke is, correct? IE, if it was perpendicular to the ground it would have to move forward?

I'm not sure I understand what you mean by where the spoke is.

Here is a picture with the same idea. P1 makes it go right (backward). P2 makes it go left (forward).


*edit* oops, here

That picture doesn't work. The center of rotation is in the center of the wheel.
I just tried this experiment with a cd spindle cover. I taped a USB cable onto it and tugged on it. The cd spindle turned CCW.
Not sure if the wheel would roll forwards if there was infinite friction meaning no slippage. But it's confirmed that the wheel will spin CCW given that force P was applied.

I'm sorry but you're just wrong. The center of rotation is the contact point at the ground. And, you're doing the experiment wrong if it turned ccw.