3. ________________:
Find the acceleration of a block of mass m
on a ______________ ramp that makes an angle q
with the horizontal.
Inclined Plane
frictionless FN a
a =
Fnet/m
w = mg q
Fnet
To determine a, you need ______, which means
you need the ___________ that act on the block.
forces

4. To find the force that accelerates the block down
the incline, you need to choose new axes that are
______________ ( ) and __________________( )
to the plane’s surface.
parallel ||
perpendicular
Notice:
The incline
angle ____
is _________
as this one.
New
Axes:
perpendicular q
the same FN
parallel || q || w q

5. The__________________ and _________________
components of ____ are the sides of a ___________
triangle:
perpendicular
parallel
right w
w||
adjacent
side q || w┴
hypotenuse
opposite w
side w┴
adj
hyp =
= ______
cosq 
w┴ = ________
wcosq w
w||
opp
hyp
w|| = _________
wsinq =
= _______
sinq  w

6. Now return to the full
free body diagram
and replace ____ by
its ________________. FN w
w|| =
________
components
wsinq
w┴ =
_______ q ||
wcosq w FN FN
____ is balanced by _____:  ___ = _________ w┴
wcosq
___ is unbalanced and equals Fnet = ______________
w||
wsinq

7. So what is the acceleration a?
w sinq
mg sinq
a = Fnet m
_______ m
_______ m = = =
gsinq
mass
Notice that the result is independent of ________ .
Ex: Find the acceleration of a 0.4-N block down
a frictionless incline if the angle is 100.
Test: release from rest:
d = vit + (1/2)at2
d =
a =
a =
gsinq
a =
(9.81m/s2)sin100
(1/2)at2
2d/t2
a =
1.7 m/s2

8. To see if the equation a = _________ makes
gsinq
To see if the equation a = _________ makes
sense for the incline, see what happens when
q has the "_______________ " values:
extreme
Case 1: What is a if q = 900?
a =
gsinq
_____
free
fall
gsin900 =
900 g =
g ·1 =
Case 2: What is a if q = 00?
a =
gsinq =
gsin00 =
constant v

9. Now solve the problem, but with the block
_________ or moving with __________________due to
_____________.
at rest
constant v
friction, Ff. FN FN Ff Ff
w|| q w┴ w w q
If the block is not moving, Fnet = ___ , which
means all forces must ____________________ .
be balanced
FN = ____ = _________ (equilibrium as before). w┴
wcosq
Ff = ____ = _________ (now in __________________).
w||
wsinq
equilibrium

10. Ex. A 3.0-kg block rests on an incline that makes
an angle 300 to the horizontal. Determine the
magnitude of the normal force and the friction
force acting on the block.
3(9.81)
w =
____ = __________
__________ mg
29 N
300 w┴
wcosq
FN = ____ = _________ = _____________ = __________
(29 N)cos300
25 N
Ff = ____ = _________ = _____________ = __________
w||
wsinq
(29 N)sin300
14.5 N

11. C. Summary of inclined plane basics
Without friction:
With friction and at rest
or constant v: FN FN Ff
w||
w|| q q w┴ w┴ w w w┴
wcosq w┴
wcosq
same
FN = ____ = _________
FN = ____ = _________
Ff = ____ = _________
w||
w||
wsinq
Fnet = ____ = _________
wsinq
___ = _________ a
gsinq
Fnet = __

12. Ex: If there is friction, but the block is ____________________ ,
it must be that _____ > _____ .
In that case, the net force
Fnet = ________ FN
accelerating
w|| Ff Ff
w|| q
w|| - Ff w┴ w
Ex: Notice that the incline __________ or weakens
gravity because it is not _______________ , but only
the ________________________
that is pulling the block
along the __________
of the incline.
dilutes
w itself
parallel component of w
w||
surface w

13. Final notes: 1/ On a horizontal surface: FN = ____ w BUT,
On an incline (either
with or w/o friction): FN
FN = w┴ = ______
and NOT:
FN = ____
wcosq
w|| q w┴ w w

14. 2/ What happens to Ff and FN if q is increased and the block
remains the same and at rest? Ff FN w┴
w|| FN
original
incline: w Ff
w|| q w┴ w
inc. q q
decreases
FN __________
Ff ___________
w ____________
As _____
increases: q
increases
is the same