# Acceleration without sliding

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## Homework Statement

A flat book is situated on a seat in a car, which has an angel θ (if θ is zero the seat is horizontal and if it is 90 degrees it is vertical). The coefficient of static friction is μs.

(1) What is the largest forward acceleration the car can have, without the book sliding?

(2) What is the largest acceleration the car can have when breaking, without the book sliding?

## The Attempt at a Solution

(1) I set up the following equation, assuming the book can only slide backwards.

μs*( cos(θ)*m*g - sin(θ)*m*a ) = sin(θ)*m*g + cos(θ)*m*a

Isolating a here gives the right result I think, but after I attemted to solve (2) I thought about, what if the book was sliding the other way, would the equiation be

0 = sin(θ)*m*g + cos(θ)*m*a + μs*( cos(θ)*m*g - sin(θ)*m*a )

Isolating a here gives an expression that doesn't really make sense to me.

(2) I set up the following equation, assuming the book can only slide forward.

μs*( cos(θ)*m*g + sin(θ)*m*a ) = cos(θ)*m*a - sin(θ)*m*g

Isolating a here gives a similar result that I can't figure out. At certain angles the acceleration becomes infinite.

Am I making a fundamental error somewhere, or am I just failing to see the logic in the results I am getting?