Level 3 Forces Problem - Coefficient of Static Friction

[PeachBanana]

Homework Statement

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?

Homework Equations

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

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?

 

[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

 

[PhanthomJay]

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.

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

 

[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?

 

[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