Transcript Slide 1

Ex. A block is pulled along a frictionless table by a
force that makes an angle q to the horizontal.
F
F
FN
q
2.0
kg
w = 20 N
components
a/ Find the x- and y-________________
of F.
b/ Replace F in the free body diagram with them:
F
Fy =
Fsinq
q
Fx = Fcosq
FN
Fy
balanced
w
Fx
unbalanced
y-direction: Because the block is not accelerating
up or down, the y-forces are ________________.
balanced
equilibrium:
w = FN + Fy
Notice: w _____
≠ FN
unbalanced
x-direction: Only 1 force _________________
ax =
Fx/m = Fcosq/m
What will happen to a
if q is increased?
F
Fy
q
Fx
F
Fy
inc q
Fx
Fx ___creases,
de
also
so a ________
decreases
_____________.
Inclined Plane
________________:
A. Find the acceleration of a block of mass m
frictionless
on a ______________
ramp that makes an angle q
with the horizontal.
FN
a = Fnet/m
a
w = mg
q
Fnet which means
To determine a, you need ______,
forces
you need the ___________
that act on the block.
To find the force that accelerates the block down
the incline, you need to choose new axes that are
parallel
______________
( ||) and __________________(
)
perpendicular
to the plane’s surface.
Notice:
New
Axes:
perpendicular
FN
q
w
q
The incline
q
angle ____
the same
is _________
as this one.
perpendicular and _________________
parallel
The__________________
right
components of ____
w are the sides of a ___________
triangle:
w||
adjacent
side
q
w┴
hypotenuse
w
adj =
hyp
w┴
w
opp =
hyp
w||
= _______
sinq 
w
cosq 
= ______
opposite
side
wcosq
w┴ = ________
wsinq
w|| = _________
Now return to the full
free body diagram
w by
and replace ____
components
its ________________.
FN
w|| =
wsinq
________
q
w┴ =
wcosq
_______
w
FN is balanced by _____:
FN = _________
w┴
wcosq
____
 ___
wsinq
w|| is unbalanced and equals Fnet = ______________
___
So what is the acceleration a?
a = Fnet =
m
w sinq =
_______
m
mg sinq = gsinq
_______
m
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.
a = gsinq
a = (9.81m/s2)sin100
a = 1.7 m/s2
Test: release from rest:
d = vit + (1/2)at2
d = (1/2)at2
a = 2d/t2
a=
a=
gsinq makes
To see if the equation a = _________
sense for the incline, see what happens when
extreme
q has the "_______________
" values:
Case 1: What is a if q = 900?
a = gsinq
= gsin900
= g ·1 = g
free
_____
fall
_____
Case 2: What is a if q = 00?
a=
gsinq = gsin00
constant v
=
0
900
B. Now solve the problem, but with the block
at rest or moving with __________________due
_________
to
constant v
_____________.
friction, Ff.
FN
F
N
Ff
Ff
w||
q
w┴
q
w
w
0 , which
If the block is not moving, Fnet = ___
be balanced
means all forces must ____________________
.
wcosq (equilibrium as before).
w┴ = _________
FN = ____
w|| = _________
wsinq
Ff = ____
(now in __________________).
equilibrium
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.
w=
300
3(9.81)
mg = __________
____
29 N
__________
wcosq = _____________
25 N
w┴ = _________
(29 N)cos300 = __________
FN = ____
w|| = _________
(29 N)sin300 = __________
14.5 N
Ff = ____
wsinq
= _____________
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
wcosq
w
F
=
____
=
_________
same
┴
wcosq
w
N
FN = ____
┴ = _________
w|| = _________
Fnet = ____
wsinq
a = _________
___
gsinq
w|| = _________
Ff = ____
wsinq
0
Fnet = __
Ex: If there is friction, but the
accelerating
block is ____________________
,
Ff
w|| > _____
it must be that _____
.
In that case, the net force
w|| - Ff
Fnet = ________
FN
Ff
w||
q
w┴
w
dilutes or weakens
Ex: Notice that the incline __________
w itself
gravity because it is not _______________
, but only
parallel component of w
the ________________________
that is pulling the block
along the __________
surface
of the incline.
w||
w
Final notes:
1/ On a horizontal
w
surface: FN = ____
FN
w
BUT,
On an incline (either
with or w/o friction):
wcosq
FN = w┴ = ______
and NOT:
FN = ____
w
FN
w||
q
w┴
w
2/ What happens to Ff and FN
if q is increased and the block
remains the same and at rest?
Ff
FN
w┴
original
incline:
q
w||
FN
w
Ff
w||
q
w
w┴
inc. q
decreases
FN __________
q
As _____
increases
Ff ___________
increases:
is the same
w ____________
Open your 3-ring binder to the
Worksheet Table of Contents.
Record the title of the worksheet:
Inclined Plane WS