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K.~r
A.
Student
Class
Date
_
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Vertical Circular Motion 3
./ Vertical circular motion occurs when an object, such as a motorcycle, moves
on a vertical circular path .
./ The speed of the object varies, and so do the magnitudes of the centripetal
acceleration and centripetal force .
./ Since there is a change of speed, tangential acceleration is present in a vertical
circular motion .
./ In a vertical circular motion we must consider the gravity force. We must
consider the normal force as well if there is contact between objects.
A carnival
clown rides a motorcycle
down a ramp and around a
"loop-the-loop".
If the loop has a radius
of 18 m, what is the
slowest
speed the rider can have at the top of the loop and avoid
falling?
1.
- V"".o.\;o.,rcyc!
~
~et
A 2.a kg object
vertical
circle
2.
cw
•
-
LQ. IV
.
?.V\A
W1
(]
Fr
~
string
fc -=
-
,.-'0..() C
when the
F,.
VV'L
-
in the
o.c..
\Jt
\'V\-
,.
~
v"2.=~'Y
ca -= 1- ~
V:
(;r
~r,'3
L__
~~
OM.
h]
and swung in a
object
is
at the
'M.~
;!
-+ """
1-
r, :::2.0 ''gC".8/~
y-
string
-=
)-t
2.0\(.3 (12.""'/12
1.5 ~
[FT =: 2. I 2?J
when the
object
is
at the
'l.
=
M.
ac
F~- F,. -= -
f
FlJ + T=~
FT ~
1'\'\
(J'
'f'I\ (). C-
fT -= Fqd,+ -:;:-
the tension
path?
(~"":
F"c
we
L
f
0cHo>tV-
't ~
t1\
.sr~i'OI.
'M \J 1.
b) What is
top of its
'I
So \ oW'e5,
in the
:
F',.
"'"f.
CAd )L we w~~\
C~~\
\-'-'e.
is attached
to a 1.5 m long string
at a constant
speed of 12.a m/s.
a) What is the tension
bottom of its path?
2."'-lA
v-/
-("'0
Fe:;::
:
~ -- F.:(j-NF",,~D
e
clOI.\JVI
-+- \""e
-)-~-:-F::~-
""-~lie
laar
v ('Irt,'co.. I
+0 r
+"'.e.
Ai
f="l
-
""'- ~
L.
'M.f
2.,Ok.S
..
((z.o ...•/sl - 2..D~{~.811&.}
t.SW\
\J~
~v':_ fca
-:::"'"V y-
(;f
lei
,...112 t.J-:
~J
(M.l..•.
l""u~
--
te 5t-OI-l)
lA
3.
The condition of apparent weightlessness for the passengers can
be created for a brief in~tant when a plane flies over the top of
a vertical circle. At a speed of 215 m/s, what is the radius of
the vertical circle that the pilot must use?
F"" -:: 0
~
1'\0+
>0
I
(p\.l01
doe>
pl1~h 0""
s e C\ t
",ot
;
+-~e
"~~ S e" t J.
r",~h
~"'C'/£)
~CLt"7 \0 """]
4.
A roller coaster at an amusement park has a dip that bottoms out
in a vertical circle of radius r. A passenger feels the seat of
the car pushing upward on her with a force equal to twice her
weight as she goes through the dip. If r=28.8 m, how fast is the
roller coaster traveling at the bottom of the dip?
d
+~~frobl.(W\)
'Py
(~~"eV\
F",::: 2.F
h ==
~
.--,- ,
Fe ~ VV\ ~c
2.""~ Le;..vJ
FN- F~~ ,~ ~
..•.
zF~ - F~ -=
fV\
&= (~r :::E~/>]
~~~
co {t(l.€.' "'{ION
~
a) Find the magnitude of the centripetal force •
.
F;~+ F",
Fc=
~~z.. \C~
-=,..V'I\:::L-'r
L
('Z.~'sY
\'2..bv-
b) Find the normal force that acts on the cycle.
f~ +
FroJ -:::
Fe
FrJ -= Fe - F~
~~
_
l. '?7~
1,000)<
lOt,
r
' ~~ ~ ~~
y-
A moto~~ycle has a constant speed of 25.0 m/s as it passes over
the top of a hill whose radius of curvature is 1~6 m. The mass of
the motorcycle and driver is 342 kg.
5.
V ~
,~z.
",l
(q. ~ I )
0 l'>
6.
A child is moving at constant speed in a vertical circle on a
ferris wheel.
Top
(
)
Bottom
':
a) On the diagram, sketch and label arrows to represent the
gravitational force, and the normal force acting on the child at
the bottom of the ride. What is the centripetal force here?
Fe
Frv ,- f~ )
=::
b) On the diagram, sketch and label arrows to represent the
forces acting on the child at the top of the ride. What is the
centripetal force here?
Fe
-= F~- r,..;
c) Write the Newton's second law for the bottom of the ride.
F: "'F;o._ m
C
c
0- C
0,--~_'"
f~
""_;_l.--,}
d) Write the Newton's second law for the top of the ride.
- Fe ~ - IN'\ ttc
fN
',-
f~-:::
_ """
a.. c
(FN - F~-
- •• ~