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analyzing forces
using free-body diagrams
1. imagine two books sitting at rest
on top of each other on a table.
the top book has a mass of 2 kg,
the book under the top book has a
mass of 3 kg, and the table has a mass
of 20 kg. clearly there is a force of
gravity (weight) on all three objects.
in addition, because some of the
objects are in contact with other
objects, there may be forces by one
object on another object.

a) what is the acceleration of each
of the objects?

b) what is the force of gravity
on each object?

c) what is the force on each object by
the other objects?

A) Gravity acceleration; B) 19.62[N], 29.43[N], 196.2[N]; C) 196.2[N], 225.63[N], 421.83 [N]

Explanation:

according to the statement of the problem the three books are in balance since there is no movement of any of them.

A)

The only acceleration that exists is gravitational acceleration, but this does not exert any movement on the books as they are found on a flat surface, where there is no movement.

B)

For the 2[kg] book

F1 = m*g

where:

m = mass of the book = 2 [kg]

g = gravity = 9.81[m/s^2]

F = 2*9.81 = 19.62[N]

for the 3[kg] book

F2 = 3*9.81 = 29.43[N]

For the table:

F3 = 20*9.81 = 196.2[N]

C)

To find the force we must analyze each of the bodies separately and establish equilibrium conditions, i.e. the sum of forces on the vertical axis must be equal to zero

For the 2 [kg] book

N1 - mg = 0

N1 = mg

N1 = 20*9.81 = 196.2[N]

Now this normal force is exerted over the 3[kg] book. We analize the forces acting over this book.

-N1 - mg + N2 = 0

N2 = (3*9.81) + 196.2

N2 = 225.63[N]

And the table will receive the normal force N2, so the normal force exerted by the floor over the table will be.

-N2 - mg + N3 = 0

N3 = 225.63 + (20*9.81)

N3 = 421.83 [N]

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