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?
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?