Free Body Diagram
Force Vectors

Force is a vector.

A block sliding on an inclined plane has forces acting
on it.

We know there is a force of gravity and normal force.
q
Force Diagram

Draw the forces acting on
the block.

The force of gravity points
down with magnitude Fg=mg.

The normal force points
away from the surface of the
inclined plane.
FN
q
Fg  mg
Force Diagram
iˆ

Draw components of the
forces so the vectors can be
added.

The coordinates should point
along the surface.
FN
mg sin q
• The normal force is
unknown
• The motion will be along the
surface
q
mg cos q
Fg  mg

The components of Fg are
compared to the surface.
Net Force

FN
• No motion or acceleration
away from the surface
• No force in that component
mg sin q
q
mg cos q
The block stays along the
plane.

Solve for the normal force:

FN  mg cosqˆj

Net force:


Fg  FN  mg sin qiˆ
Fg  mg
Motion from Force



The net force causes the block to accelerate.
The amount of acceleration is force divided by mass.
This is a constant acceleration moving the block.
a
q
F
 g sin q
m
Inclined Plane

Pushing a block up an
incline is easier than
lifting.
Fapp  mg sin q

To get constant velocity
a force equal to the
downward acceleration
must be applied.
FN
mg sin q
q
mg cos q
Fg  mg
Mechanical Advantage


The inclined plane has been
used as a machine for
centuries.
Pushing a block up an
incline is easier than lifting.
mg
mg sin q
q

The ratio of the force to lift
directly compared to the
force using the incline is the
mechanical advantage.
mg
1

mg sin q sin q
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