# Static Friction Can Cause Motion

1. Mar 31, 2013

### IamMoi

1. The problem statement, all variables and given/known data

Two people start running from rest. The first person has a mass of 59 kg and is wearing
dress shoes with a coefficient of static friction of 0.52. The other person is wearing
running shoes with a coefficient of static friction of 0.66.
Explain why we do not really need the mass of either person when finding the initial maximum possible acceleration

Mass1= 59 kg
μ1= 0.52
μ2= 0.66
V1i=V2i= 0m/s
Mass2[\B] =?
2. Relevant equations
Ff=μFn
d= vit+1/2at^2

3. The attempt at a solution
mass is not needed because the initial velocity of the two people is 0m/s, but when I calculated the acceleration of the first person the acceleration is not equal to zero.

2. Mar 31, 2013

### cepheid

Staff Emeritus
Welcome to PF IamMoi!

In the phrase "initial maximum possible acceleration", the key word is maximum. Consider this question: what determines the maximum? Why could a person not accelerate faster than this? What would happen if he tried?

3. Mar 31, 2013

### IamMoi

does that mean that velocity at this point is 0?

4. Mar 31, 2013

### cepheid

Staff Emeritus
Uhh...you didn't actually answer any of my questions. Anyway: "maximum possible acceleration" means that the acceleration cannot be larger than this value. Can you think of a reason why not?

5. Mar 31, 2013

### IamMoi

you cannot exceed the maximum..
will the solution be like this ...
force=mass*acceleration
Ff=μmg
F=m*a

Ff=F
μmg=ma
a=μg?

6. Mar 31, 2013

### cepheid

Staff Emeritus
The reason why "walking" works at all is because when your foot pushes backwards on the ground, by Newton's 3rd Law, the ground pushes forwards on your foot, and this is the force that propels you forward. The force arises because of static friction. The motion of your feet is such that your foot wants to slide backwards relative to the surface of the ground, and static friction prevents this sliding from happening. But it prevents it only up to a limit. What would happen if you tried to exceed this limit? I.e. what if you pushed backward too hard on the ground?

7. Mar 31, 2013

### IamMoi

you will slide???

8. Mar 31, 2013

### cepheid

Staff Emeritus
Exactly. If you push too hard, the force will overcome static friction, and your feet will just slip (meaning slide backwards across the surface).

So, THAT (the amount of static friction available) determines the largest possible force, and therefore the largest possible acceleration.

From this information, you should be able to calculate the largest possible acceleration, and you will see why the mass doesn't matter in this calculation. TRY IT.

9. Mar 31, 2013

### IamMoi

Acceleration for the first person:

a=μg
= 0.52*9.8
=5.096 m/s^2
Acceleration for the second person
a=μg
=0.66*9.8
=6.468m/s^2

10. Mar 31, 2013

### cepheid

Staff Emeritus
Not going to bother checking your numbers since that isn't what the question is asking. The equation a = μg is correct, but the important thing is *where did you get this equation from?* The answer to that will answer the question of why you don't need the mass of either person to compute the max acceleration.

11. Mar 31, 2013

### IamMoi

ohhh.... is it because the maximum static friction will be equal to the net force???

12. Mar 31, 2013

### cepheid

Staff Emeritus
Yes exactly. Net force: F = ma.

Static friction F = μN = μmg

If you equate these two F's, what happens to m?

13. Mar 31, 2013

### IamMoi

they both cancel

14. Mar 31, 2013

### cepheid

Staff Emeritus