08prob_11

08prob_11 - Assigment #8, 5/13/11 Page 1 of 3 UC Davis...

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Unformatted text preview: Assigment #8, 5/13/11 Page 1 of 3 UC Davis 155° a t v a c r√ v√ c) r√ v√ r√ v√ a) b) r√ F√ (a) 155° a t v a c r√ v√ c) r√ v√ r√ v√ a) b) r√ F (a) Physics 9A-C Assignment #8 Cole [9.64]

a)

Curl
the
fingers
of
your
right
hand
in
the
direction
of
 the
rotation
of
the
wheel.

Your
thumb
points
out
of
the
page,
so
 ∑√ 
points
out
of
the
page. b)

For
the
magnitude,

 v = ds dt = r d θ dt = r ω .

Place
the
fingers
of
 your
right
hand
along
∑√,
coming
out
of
the
page,
and
turn
your
 hand
so
the
normal
to
your
palm
faces
the
direction
of

 r√.
 

Your
 thumb
will
now
point
in
the
direction
of
 v√.

õ

v√
=
∑√
ª
r√ 

 c)

Place
the
right
hand
fingers
along
∑√,
out
of
the
page,

palm
 facing
 v√ ,
and
the
thumb
points
radially
inward.

For
the
 magnitude,
 a c 
=
∑v
=
∑(r∑)
=
r∑ 2 ,
 
so
∑√
ª
 v√ 

has
the
correct
magnitude
and
 points
radially
inward. [9.66]

a)
 ω = d θ dt = d γ t 2 − β t 3 ( ) dt = 2 γ t − 3 β t 2 b)

 α = d ω dt = d 2 γ t − 3 β t 2 ( ) dt = 2 γ − 6 β t 



c)

Max
∑
occurs
 where
d∑/dt
=
0
so
å
=
0. 2 γ − 6 β t 
=
0

õ

 t = γ 3 β = 3.2 rad/s 2 3 0.5 rad/s 3 ( ) 

=

2.13
s. At
this
time,

 ω = 2 3.2 rad/s 2 ( ) 2.13 s ( ) − 3 0.5 rad/s 3 ( ) 2.13 s ( ) 2 

=

6.83
rad/s.

 [9.69]

a)

The
angular
acceleration
is

 α = a t r = 3 m/s 2 60.0 m 
=
0.05
rad/s 2 . b)

∑
=
åt
=
(0.05
rad/s)(6
s)
=
0.3
rad/s.

c)

The
radial
acceleration
is
centripetal
acceleration,
 so

 a c 
=
r∑ 2 
=
 (60
m)(
0.3
rad/s) 2 
=

5.4
m/s 2 . d)

The
angle
the
car
makes
is

oe
=
∑t
+
(1/2)
åt 2 

=
(
0.3
 rad/s)
(6
s)
+
(1/2)(0.05
rad/s 2 )(6
s) 2 
õ oe

=

2.7
rad
=
155°

see
figure. e)

 a = a t 2 + a c 2 = 3 m/s 2 ( ) 2 + 5.4 m/s 2 ( ) 2 
=
6.18
m/s 2 .
 Í F√

=

ma√

õ

F
=
 (1240
kg)(6.18
m/s 2 )
=
7.66
kN....
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This note was uploaded on 09/28/2011 for the course PHY 9A taught by Professor Svoboda during the Spring '08 term at UC Davis.

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08prob_11 - Assigment #8, 5/13/11 Page 1 of 3 UC Davis...

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