Recitation ClassWork 4 solutions
Physics 203
1.
Chapter 5 problem 5
REASONING
The magnitude
a
c
of the car’s centripetal acceleration is given by Equation 5.2 as
2
c
/
a vr
=
,
where
v
is the speed of the car and
r
is the radius of the track. The radius is
r
= 2.6
×
10
3
m. The speed can
be obtained from Equation 5.1 as the circumference (2
π
r
) of the track divided by the period
T
of the
motion. The period is the time for the car to go once around the track (
T
= 360 s).
SOLUTION
Since
2
c
/
=
and
( )
2/
v
rT
=
, the magnitude of the car’s centripetal acceleration is
( )
( )
2
23
22
2
2
c
2
2
4
2.6 10 m
4
0.79 m/s
360 s
r
vr
T
a
rr
T
×
=
=
=
=
=
2.
Problem 11
The sample makes one revolution in time
T
as given by
T
= 2
r
/
v
. The speed is
v
2
=
ra
c
= (5.00
×
10
–2
m)(6.25
×
10
3
)(9.80 m/s
2
)
so that
v
= 55.3 m/s
The period is
T
= 2
(5.00
×
10
–2
m)/(55.3 m/s) = 5.68
×
10
–3
s = 9.47
×
10
–5
min
The number of revolutions per minute = 1/
T
= 10 600 rev/min .
3.
Problem 22. Before you try to answer this problem mathematically, first draw a force diagram. Once you and your
group think you have the diagram right, call your TA over and discuss it with them. If you’re TA isn’t available
because they are working with another group, find another group in the class to discuss your ideas with.
REASONING
The coefficient
µ
s
of static friction is related to the magnitude
MAX
s
f
of the maximum static
frictional force and the magnitude
F
N
of the normal force acting on the car by
MAX
s
sN
fF
=
(Equation
4.7), so that:
MAX
s
s
N
f
F
=
(1)
The car is going around an unbanked curve, so the centripetal force
2
c
mv
F
r
=
(Equation 5.3) must be
horizontal. The static frictional force is the only horizontal force, so it serves as the centripetal force. The
maximum centripetal force occurs when
MAX
cs
Ff
=
. Therefore, the maximum speed
v
the car can have
without slipping is related to
MAX
s
f
by
2
MAX
mv
r
=
(2)
Substituting Equation (2) into Equation (1) yields
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 Fall '08
 RICHARDSON, B
 Physics, Acceleration, Force, Friction, Work, m/s, centripetal force Fc

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