can someone help me with this question?

Question

a student pushes a 0.85-kg textbook across a cafeteria table toward a friend. As soon as the student withdraws the hand (the force is remobed), the book starts slowing down, coming to a stop after moving 65 cm horizontally. The coefficient of kinetic friction between the surfaces in contact is 0.38.

a) how do i draw a system diagram and an FBD diagram of the book as it slows down and calculate the magnitudes of all forces in the diagram.

b) Calculate the work done on the book by the friction of the table.


thanks for any help!

Answer 1

a)Draw a force opposite to the motion name it friction
Draw the weight and reaction forces vertically acting opposite to each other .

b) Work done on book by friction = Force X distance
Force = friction = (0.38X0.85X9.8)
Distance = (0.65 m).

Work done = (-0.38X0.85X9.8) X (0.65) = - 2.05751 J.

Look , There is a work done on the friction . so work done by the friction force is negative .

Answer 2

At the instant the student withdraws the hand, the forces on the book are

mg, directed down
N, directed up
uN, directed back (u is the coefficient of friction)

Newton's Second Law in the vertical dimension tells us that

N = mg

so the friction force is

uN = umg

The book slides 65 cm, so

2 a ( .65 m ) = vo^2

Solve for the acceleration of the book. Then F = ma gives you the friction force and F ( .65 m ) the work done by friction.