Static Friction Can Cause Motion

[IamMoi]

Homework Statement

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] =?

Homework Equations

Ff=μFn
d= vit+1/2at^2

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.

 

[cepheid]

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?

 

[IamMoi]

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?

does that mean that velocity at this point is 0?

 

[cepheid]

does that mean that velocity at this point is 0?

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?

 

[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?

 

[cepheid]

I have no idea, sorry

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?

 

[IamMoi]

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?

you will slide?

 

[cepheid]

you will slide?

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.

 

[IamMoi]

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.

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

 

[cepheid]

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

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.

 

[IamMoi]

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.

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

 

[cepheid]

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

Yes exactly. Net force: F = ma.

Static friction F = μN = μmg

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

 

[IamMoi]

Yes exactly. Net force: F = ma.

Static friction F = μN = μmg

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

they both cancel

 

[cepheid]

they both cancel

Thus answering the question in your original post.

 

[IamMoi]

Thus answering the question in your original post.

oh... Thank you