Static friction and acceleration

[goonking]

Homework Statement

A glass of orange juice is on the floor of a subway car traveling along a straight path at constant velocity. The coefficient of static friction between the glass and the floor is 0.32. The subway suddenly accelerates forward. What is the maximum acceleration that the subway car can have without the orange juice sliding backward on the floor

Homework Equations

Fs = μ FN

The Attempt at a Solution

So we want the juice to stay still. So the FN x μ cannot become equal or greater than Fs, correct? How would we approach this problem without a mass given for the juice?

 

[NascentOxygen]

Denote the mass as m kg, and proceed as you have outlined.

 

[goonking]

Denote the mass as m kg, and proceed as you have outlined.

so FN = m x mg?

 

[AlephNumbers]

What is Newton's third law?

 

[goonking]

What is Newton's third law?

For every action, there is an equal and opposite reaction.

 

[NascentOxygen]

so FN = m x mg?

Using F = m.a you get F_N = m.g

 

[goonking]

Using F = m.a you get F_N = m.g

yes, so now Fs = μ mg but we still have 2 unknowns

 

[NascentOxygen]

yes, so now Fs = μ mg but we still have 2 unknowns

Proceed to determine maximum acceleration undaunted ...

 

[goonking]

.32 x g = .32 x 9.8 m/s^2 = 3.136, that's the answer, thanks!

 

[NascentOxygen]

.32 x g = .32 x 9.8 m/s^2 = 3.136, that's the answer, thanks!

You should have kept the m in your expressions, and at the end shown they cancel, rather than letting them disappear without explanation.

 

[goonking]

You should have kept the m in your expressions, and at the end shown they cancel, rather than letting them disappear without explanation.

ok, ill remember that