# Level 3 Forces Problem - Coefficient of Static Friction

1. Feb 11, 2012

### PeachBanana

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

A coffee cup on the dashboard of a car slides forward on the dash when the driver decelerates from 48 km/hr to rest in 3.7 s or less, but not if he decelerates in a longer time.

What is the coefficient of static friction between the cup and the dash?

2. Relevant equations

Final Velocity - Initial Velocity / Time
Coefficient of Static Friction = Maximum Force of Static Friction / Normal Force
F = ma?

3. The attempt at a solution

I found a. Final Velocity - Initial Velocity / Time

a = -3.59 m/s^2

I was going to attempt to use F = ma but I have two unknowns - mass and net force. If the coffee cup is decelerating, the direction of the net force is pointing downward. In a free body diagram, we know mg always points straight down. I also think that force is larger than the normal force because the acceleration is negative which means the direction of net force is down. Could someone give me a hint as to how I can figure out the normal force? Or if I'm doing this right at all?
1. The problem statement, all variables and given/known data

2. Relevant equations

3. The attempt at a solution

2. Feb 11, 2012

### wukunlin

hint: force on the cup during deceleration equals static friction force

if you still don't get it, write down the statement above mathematically

3. Feb 11, 2012

### PhanthomJay

The car is decelerating forward, not down. There is no acceleration in the up-down vertical direction.

4. Feb 12, 2012

### PeachBanana

I still don't think I understand. I'll say left is the negative x direction and right is the positive x direction. In my free body diagram I left out vertical forces because the acceleration is occurring in the x axis. I have a force vector pointing to the left that says F = m (-3.59 m/s^2) and then one going right that says F sub k for kinetic friction. I have attached a diagram for clarification. I also noticed on my left side I'm missing a mass. Is that even relevant to this problem?

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5. Feb 13, 2012

### wukunlin

if you equate the force during decelerating to the static friction force, you will see the mass of the cup (and the normal/weight force) is irrelevant to finding the answer of this question