- #1

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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 μ

_{s}.

(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.

μ

_{s}*( 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 + μ

_{s}*( 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.

μ

_{s}*( 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?