# Homework Help: Static friction and acceleration

1. Mar 5, 2015

### goonking

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

2. Relevant equations
Fs = μ FN

3. 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?

2. Mar 5, 2015

### Staff: Mentor

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

3. Mar 5, 2015

### goonking

so FN = m x mg?

4. Mar 5, 2015

### AlephNumbers

What is Newton's third law?

5. Mar 5, 2015

### goonking

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

6. Mar 5, 2015

### Staff: Mentor

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

7. Mar 5, 2015

### goonking

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

8. Mar 5, 2015

### Staff: Mentor

Proceed to determine maximum acceleration undaunted ......

9. Mar 5, 2015

### goonking

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

10. Mar 5, 2015

### Staff: Mentor

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

11. Mar 6, 2015

### goonking

ok, ill remember that