Solving the Inclined Plane Homework Problem

[rechitzy]

Homework Statement

An inclined plane at 30.0° is 4.9 m long. A book which has a coefficient of kinetic friction with the inclined plane of 0.16 is placed at the top and immediately begins to slide. How long will it take for the book to reach the bottom of the incline?

Homework Equations

a=mg sin(angle)-coeff of kinetic friction cos(angle)

t2= Xf/(1/2)(a)

The Attempt at a Solution

i tried it and i have had different answers every time due to some mistakes, but i have only one attempt left.

 

[AtticusFinch]

Ok, first you need to draw a force diagram for the object.

The book has a normal force exerted by the incline on the book. It has a component of gravity in the direction perpendicular to the incline. It has a component of gravity in the direction parallel to the incline. There is a force of friction acting on the book due to the incline and points in the direction opposite to the force of gravity parallel to the incline.

This problem involves friction. It is important to know the normal force in all friction problems so let's find that first.

You know the book is not floating off the incline so the normal force which points in a direction perpendicular to the incline must equal the component of gravity pointing in the opposite direction. Therefore,

N = mgcos30 and Fric = 0.16mgcos30

This force of friction opposes the force of gravity acting parallel to the incline, so Newton's second law in the direction parallel to the incline gives us

mgsin30 - Fric = ma

We know Fric from earlier.

mgsin30 - 0.16mgcos30 = ma

Notice all terms have a "m". Cancel them out.

gsin30 - 0.16gcos30 = a

Solve for your acceleration.

The book has no initial velocity, and is displaced 4.9 m. By kinematics,

4.9 = 0.5at²

You know a from earlier, so solve for t.