Physics friction problem

1. Aug 28, 2008

ritwik06

1. The problem statement, all variables and given/known data
A man tries to walk on ice[Very less friction]. He takes small steps rather than large ones. Why?

3. The attempt at a solution
I think he should have taken longer steps in order to reduce the normal reaction and consequently the friction which ensures low velocity. What's wrong with this?

2. Aug 28, 2008

stewartcs

Re: Friction

Think about the angle his legs will make with the ice when taking small steps versus large steps.

HINT: He wants to increase the frictional force, not decrease it, to keep from sliding.

CS

3. Aug 28, 2008

ritwik06

Re: Friction

Thats the clinch. I have a clear picture of the angle, the normal and verything.

I just cannot understand this thing:
He wants to increase the frictional force, not decrease it, to keep from sliding.

4. Aug 28, 2008

ritwik06

Re: Friction

The thing is that I was doing my book exercises, I encountered this:
Objective:
While walking on ice, one should take small steps to avoid slipping. This is because smaller steps ensure:
1. larger friction
2. smaller friction
3. larger normal force
4. smaller normal force
Th answer given is (2. smaller friction). The book is written by a well known writer and its difficult for me to understand what actually happens. Please help me.

5. Aug 28, 2008

LowlyPion

Re: Friction

Frictional force is proportional to the weight straight down into the ice. The greater the step the greater the horizontal force that must be accounted for by friction to prevent slipping. (Remember Bambi's first steps on the ice?)

Since with increasing angle the less friction that gets created and the more that is required ... oops.

6. Aug 28, 2008

HallsofIvy

Staff Emeritus
Re: Friction

What makes you think that longer steps would reduce the normal force? No matter how long the steps are, the normal force is his weight!

7. Aug 28, 2008

Defennder

Re: Friction

You sure that's what it says? Because that's the opposite of what you would expect the man to do if he wanted to keep from slipping. Why would he take smaller steps if it resulted in lesser friction -> greater chance of slipping?

8. Aug 28, 2008

Banaticus

Re: Friction

Your mass plus the acceleration of gravity gives a Force vector ($F_{you}$)that, when you stand straight up and down, is directly opposite the normal force, correct? But, when your legs spread wider than your shoulders (when you get an angle in there), you can decompose $F_{you}$ into a vertical and a horizontal force. Normally, when you do the splits, the horizontal component of that vector is opposed by your own leg muscles (your abductors) and by the friction of the surface. When you're on a low-friction surface (or a no-friction surface), the horizontal component of $F_{you}$ is opposed only by your own muscles, which makes walking much more fatiguing.

Now for a less physicsy explanation. ;)

True, your normal force is always your weight. But what is walking, really? Typically, it's falling (with style) -- a controlled fall. You shift your weight forward and as you fall, you bring a leg out and you land on that leg. You then shift your weight forward and as you fall you bring your other leg out and you land on that leg.

When you really don't want to fall, you can put your leg out in front of you then slowly shift your weight from leg to leg, but this is slower, it's not how we normally walk. But when you're on a low friction surface, it's easy to see that it's difficult to shift your weight from leg to leg if you're almost doing the splits, if your legs are far apart.

If you're walking like normal, it's also easier to "catch" yourself if you're only falling for a short distance, if you take smaller steps.

Also, when you take smaller steps, you don't have to use your leg muscles as much to prevent yourself from doing the splits as you're walking. Normally, surface friction helps to stop your legs from skating out from under you.

9. Aug 28, 2008

stewartcs

Re: Friction

Ah, I see what they are really after now. I think they could have posed the question a bit better though.

He will want to decrease his horizontal component of force by taking smaller steps, not the friction between his feet and the ice. The reason for this is due to the fact that the maximum static frictional force to prevent him from sliding is fixed by his weight and the coefficient of friction between the ice and his foot (I was implying that this needed to be increased to prevent slipping in my previous post). The maximum static frictional force does not change with the angle between his legs and the ice since the normal component is fixed by his weight. However, the horizontal component does change with the angle.

Hence, if he increases his angle by taking larger steps, the horizontal component of force is increased and eventually that will overcome the maximum static frictional force present between his foot and the ice, thus causing him to slide.

Note: The angle increasing or decreasing depends on where the angle is referenced from.

CS