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1
yhy does mud fly off a rapidly turning wheel?
7 '
133. Astronauts floating around inside the space shuttle
-are not actually in a zero-gravity environment. What
is the real reason astronauts seem weightless?
%4. A girlat a state fair swings a ball in a vertical circle at
i - the end of a string. Is the force applied by the string
. greater than the weight of the ball at the bottom of
the ball's path?
>:•-.
~
practice problems
39. During a solar
\se, the moon, Earth, and sun lie
on the same line, ,\ath the moon between Earth and
the sun. What force is exerted on
a. the moon by the sun?
b. the moon by Earth?
c. Earth by the sun?
(See Sample Problem 71. See the table in the appendix for data on the sun, moon, and EarthO
use.
•••••••HB^^^R
35. Tarzan (m = 85 kg) tries to cross a river by swinging
from a 10.0 m long vine. His speed at the bottom of
the swing, just as he clears the water, is 8.0 m/s.
Tarzan doesn't know that the vine has a breaking
strength of 1.0 X 10 N. Does he make it safely
across the river? Justify your answer.
(See Sample Problem 7H.)
36. Approximate the gravitational force of attraction
between a 50.0 kg girl and a 60.0 kg boy if they are
sitting 2.50 m apart in physics class.
(See Sample Problem 71.)
MIXED REVIEW PROBLEMS
40. An airplane is flying in a horizontal circle at a speed
of 105 m/s. The 80.0 kg pilot does not want his centripetal acceleration to. exceed 7.00 times free-fall
acceleration.
a. What is the minimum radius of the circular
path?
b. At this radius, what is the net force mat maintains circular motion exerted on the pilot by
the seat belts, the friction between him and the
seat, and so forth?
37. What is the gravitational force between the proton
4/
n-27
,-311 kg)
(1.67 X 10~
kg) and the electron (9.11 x ICT*
in a hydrogen atom if they are 1.00 X 10~ m apart?
(See Sample Problem 71.)
38. A 515 kg roller-coaster car rolls down past point A
and then up past point B, as shown in Figure 7-17.
a. If the vehicle has a speed of 20.0 m/s at point
A, what is the force of the track on the vehicle
at this point?
b. What is the maximum speed the vehicle can
have at B for gravity to hold it on the track?
, (SeeiSample Problem 7H.)
43. A 2.00 x 103 kg car rounds a circular turn of radius
B
20.0 m. If the road is flat and the coefficient of static
friction between the tires and the road is 0.70, how
fast can the car go without skidding?
Figure 7-17
44. A 13500 N car traveling at .'50.0 km/h rounds a
curve of radius 2.00 X 10 m. ?ind the following:
a. the centripetal acceleration of the car
b. the force that maintajns centripetal acceleration
c. the minimum
icient of static friction
l^^4_,,
4.1
j.1
,
.-'• ,_1.
,
1
,1
,
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11
32. The inertia of the pieces of
mud exceeds the frictional
force that maintains the mud's
circular motion.
33. The astronauts and space
shuttle both have the same
acceleration, that of free-fall
acceleration. Because of this,
the astronauts see everything
. at rest and believe there is no
force on them.
34. Yes, the string must exert a
force equal to the ball's weight
and the circular force that
maintains circular motion.
35. no, 1.37 x 103 N > 1.0 X 103,N
36. 3.20xlO~ 8 N
47
-i 37. 1.02xlO~ N
38. a.
b. 12.1 m/s
39. a. 4.39 x 1020 N
b. 1.99xl0 2 0 N
c. 3.55xl0 2 2 N
40. a. 161m
b. 5.49xl0 3 N
41. 119 rev
42. 1.02m
43. ,12 m/s
44. a. 0.965 m/s2
b. 1.33X10 3 N
c. 0.0985
-ihe c#- r •!•»
ion s
; peta I
48. An air puck of rnass;0.025 kg is tied to a string and
allowed to revolve in a circle of radius 1.0 m on a
frictionless horizontal surface. The other end of the
string passes through a -hole in the center of the surface, and a mass of 1.0 kg is tied to it, as shown in
Figure 7-19. The suspended mass remains in equilibrium while the puck revolves on the surface.
49. In a popular amusement-park ride, a cylinder of
radius 3.00 m is set in rotation at an angular speed of
5.00 rad/s, as shown in Figure 7-20. The floor then
drops away, leaving the riders suspended against the
wall in a vertical position. What minimum coefficient
of friction between a rider's clothing and the wall of
the cylinder is needed to keep the rider from slipping?
(Hint: Recall that Fs = JJ.sFn, where the normal force
is the force that maintains circular motion.)
a. What is the magnitude of the force that maintains circular motion acting on the puck?
b. What is the linear speed of the puck?
Note
= \so
48. a. 9.8 N
b. 2.0xl0 1 m/s
49. 0.131
Figure 7-20
Figure 7-19
21 (II) In a "Rotor-ride" at a carnival, riders are pressed
against the inside of a vertical cylinder 2.8 m in
radius rotating at a speed of 3.2 rad/s when the floor
drops out. What minimum coefficient of friction is
needed so a person will not slip down?
23 (II) If the static coefficient of friction between tires
and road is 0.70, what is the minimum turning radius
on a level road for a car traveling at (a) 30 km/h, and
(6) 60 km/h?
A 05
10
b) H3
25 (III) A car rounds a curve of radius 50 m banked at
an angle of 16°. If the car is traveling at 70 km/h, will
a friction force be required? If so, how much and in
what direction? The car's mass is 1200 kg.
A" -
VQ £
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tlo u
27 (III) If a plant is allowed to grow from seed on a
rotating platform, it will grow at an angle, pointing
inward. Calculate what this angle will be (put yourself in the rotating frame) in terms of g, r, and As. V'
ft
Tar more.
Grade 12 University Physics
Practice QUIZ on centripetal force and apparent weight
'
t>*
USE g = 10 N/kg
1.
A 2.5 kg ball is being whirled in a vertical circle using a string of radius 1.6 m.
a)
If the ball is being whirled at a constant speed of 7.0 m/s, find the tension force
the top of the circle
of the string on the ball at...
the bottom of the circle
when it is 60 degrees from the
Answers .
top of the circle with respect to the
1.a)52N,102N,64N b) 4.0 m/s
vertical.
2. a) 2000 N, friction, 0.2
b)11 degrees, 10198 N
3. 1.7 m/s, 1.8s. 0.54 Hz
4.
1190N, 210 N, TOON
5. 14 N
6. 180Qbillabongs
b)
For the same radius vertical circle of 1.6 m, what is the minimum speed for the
2.5 kg ball to just complete a circle.
2.
A 1000.0 kg car moves in a circular curve of radius 200 m at a constant speed of
72km/h.
a)
If the curve is not banked, i) find the centripetal force required
ii) what real force must supply the centripetal force
• iii) find the coefficient of friction between road and car
If the curve is frictionless but banked,
i) find the banking, angle required
ii) find the normal force on the car
b)
3.
A conical pendulum moves in a horizontal circle of radius 0.5 m at an angle of
30 degrees to the vertical. Find the speed, period" and frequency.
4.
a)
c)
A 70 kg actress is in an elevator. Find her apparent weight if the elevator is...
accelerating up at 7 m/s/s
b)
accelerating down at 7 m/s/s
at constant velocity of 7 m/s [up]
5.
A 2.0 kg mass rests on a Newton spring scale in an elevator accelerating down
at 3 m/s/s. Find the reading on the spring scale.
6.
A uniform circular motion with radius 8 feet and speed 10 feet/s will produce a
centripetal .force of 50 Billabongs. (named after Fred Billabong) For the same
mass,if the radius is decreased to 2 feet, and the speed increased to30 feet/s,
how many billabongs of centripetal force will be required?
Be able to derive equations for banked curves and the conical pendulum.
7.
52. You have determined the following results when doing an
investigation. Using proportioning techniques, find the new
"Value for the centripetal force.
••"Before
After
mass = 1 ball
mass = 3 balls radius = 0.75 m
radius ==.. 1.50 m
frequency = 1.5 Hz
frequency = 3.0 Hz
centripetal force = 8.0 units
centripetal force = ? units
53. A 200 g ball on the. end of a string is rotated in a horizontal'
circle of radius 10.0 m. The ball completes 10 rotations in
5.0 s. What is the centripetal force of the string on the ball?
54. In the Bohr model of the hydrogen atom, the electron revolves
around "the nucleus. If the radius of the orbit is 5.3 x 10- m
and the electron makes 6.6 x 1015 r/s, find
(a) the acceleration of the electron and
(b) the centripetal force acting on the electron. (This force is
due to the attraction between the positively charged nucleus and the negatively charged electron?) The. mass of
the electron is 9.1 x 1Q- 31 kg.
55. A string pendulum 1.12 m long has a bob with a mass of
200 g.
(a) What is the tension in the string when the pendulum is at
rest?
.
• .
(b) What is the tension at.the bottom of the swing, if the
pendulum is moving at 1.2 m/s?
56. When you whirl a ball on a cord in a vertical circle, you find
a critical speed at the top for which the tension in the cord is
zero. This is because the force of gravity on the object itself
supplies the necessary centripetal force. How slowly can you
swing a 2.5 kg ball like this so that it will just follow a circle
with a radius of 1.5 m?
57. An object of mass 3.0 kg is whirled around in a vertical circle
of radius 1.3 m with a constant velocity of 6.0 m/s. Calculate
the maximum and minimum tension in the string.
58. Snoopy is flying his vintage war plane in a "loop the loop"
path chasing the Red Baron. His^ instruments tell him the plane
is level (at the bottom of the loop) and travelling with a speed
of 180 km/h. He is sitting on a set of bathroom scales, and
notes that they read four times the normal force of gravity
. on him. What is, the radius of the loop? Answer in metres.
(SIN '75)
>9. An Australian bushman hunts kangaroos with the following
weapon, a heavy rock tied to one end of a light vine of length
2 m. He holds the other end above his head, at a point 2 m
above ground level, and swings the rock in a horizontal circle.
The cunning kangaroo has observed that the vine always breaks
when the angle 9 (measured between the vine and the vertical)
reaches 60°. At what minimum distance from the hunter can
the kangaroo stand .with no"danger of,a-direct hit? (SIN '72)
iO. A pendulum of mass 1.0 kg is suspended from the• roof of a
•car travelling on a level road. An observer in the car notices,
that the pendulum string makes an angle of 10° with the vertical'. What is the acceleration of the car?
-.
52. 192 units
53. 3.2 X 1CP N
54. (a) 9.1 x 1022 m/s2 (b)
5S! (a) 1.96 N (b) 2.2 N
56. 3.8 m/s
57. 1.1. x IO2 N, 54 N
58. 85 m
59. 3.0 m .
60.., 1.8 m/s2