Question

Why is the following situation impossible?
a. Your 3.80-kg physics book is placed next to you on the horizontal seat of your car.
b. The coefficient of static friction between the book and the seat is 0.650, and the coefficient of kinetic friction is 0.550.
c. You are traveling forward at 72.0 km/h and brake to a stop with constant acceleration over a distance of 30.0 m.
d. Your physics book remains on the seat rather than sliding forward onto the floor.

Answer 1

Answer:

The required friction force must be at least 328.32N and the static force is only 24.7N

Explanation:

We need to compare the required friction force to the static friction force.

If we sum all forces on the book we get:

Fr = m*a

Where the acceleration can be calculated as:

$Vf^2=Vo^2-2*a*d$

$a=\frac{Vo^2-Vf^2}{2*d}=86.4m/s^2$

Replacing this value we get:

Fr = 328.32N

Now, the static friction is given by:

$Fr_e = \mu*N=\mu*m*g=0.650*3.8*10=24.7N$

Since this value is smaller than the previously-calculated required friction, we state that the book will definitely slide.