Solution Manual for Physics of Everyday Phenomena A

Conceptual Introduction to Physics 8th Edition Griffith

Brosing 9780073513904
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5 Circular Motion, the Planets, and Gravity

1 Centripetal Acceleration
2 Centripetal Forces
3 Planetary Motion
4 Newton’s Law of Universal Gravitation
5 The Moon and Other Satellites
Everyday Phenomenon: Seat Belts, Air Bags and Accident Dynamics
Everyday Phenomenon: Explaining the Tides

This chapter demonstrates the wide application of the laws of mechanics. The chapter begins considering the motion of a
ball swung in a horizontal circle. The concepts are applied next to the banking of curves and then to the motion of the planets.

Suggestions for Presentation

Motion in a circle at constant speed can be demonstrated with very simple equipment. One possibility is to use a 3/4 inch
wood dowel, 4 inches in length and with a 1/4 inch hole bored lengthwise, as a handle. A rigid plastic straw works well, too. A
nylon string passes through this handle that at one end is attached to a small weight swung in a horizontal circle and at the other
end to another weight that can move up and down. For the wooden version the top end should be beveled about the hole, sanded
smooth and waxed. Place a few marks on the string and attempt to whirl it at a rate such that the uppermost mark stays at the
bottom of your straw/tube. Try to see that the string doesn't slip up or down, so that the motion is purely circular. As you are
twirling the mass, ask your students to draw the FBDs for both the upper (twirling) mass and the lower hanging mass. The weight
attached at the bottom determines the tension in the string exerting a centripetal force on the body being whirled. With a little
practice one can whirl the body quite well at a constant speed while someone determines the time for say 50 revolutions to obtain
reasonably good quantitative results.
Then have your students predict whether 50 revs will take less time, more time, or the same time if you twirl it so that the
second mark is in line with the bottom of your tube (thus your radius of motion is larger, yet the tension is the same). Then change
the mass at the bottom, thus increasing the tension, and ask them to predict whether 50 revs at the first mark will take more time,
less time, or the same time. They should begin to get a good physical feel for the relationship between centripetal force, radius,
and speed.
This is a good place to reference everyday phenomenon box 5.1, about the centripetal force felt when the car is rolling over
in an accident.
The apparent retrograde motion of planets beyond the Earth may be a new concept to many students and is well worth
demonstrating. There are a number of applets and animations that allow you to step through the orbits of, say, Mars and Earth
while simultaneously seeing the view from Earth of Mars’ motion. Other more ambitious demonstrations could include taking your

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students outside to experience the orbits and observations themselves. While the Ptolemaic model explains the retrograde motion
very well, it fails to explain the observed variation in brightness of Mars, and thus the Copernican model is the better model, as
well as having the virtue of simplicity. You might also ask what phases of the planet Venus would be predicted with each model,
allowing students to see that the Moon is not the only object that displays phases. It turns out that the Galilean observation of the
phases and relative size of Venus is consistent with the Copernican system, as well, while inconsistent with the Ptolemaic system.
For the matter of Kepler’s Laws of Planetary motion, there is also a wealth of applets and videos on the internet. If you’re
fortunate enough to have access to a “gravity well,” (a large funnel-shaped apparatus used by some clubs to raise funds), students
can roll various objects at various angles and determine Kepler’s Laws for themselves.
Phases of the moon are clearly indicated in figure 5.21, yet students often find this diagram hard to interpret. A demonstration
with a flashlight and some spheres will help tremendously. The tides are addressed in Everyday Phenomenon Box 5.2. This gives
the instructor a chance to use Newton’s law of gravitation. The first paragraph in the analysis is often worthwhile to discuss with
students.

Debatable Issues
Some people believe that the moon landing in 1969 was just an elaborate hoax. Is this a reasonable belief? Show your
students a video of Apollo astronauts on the Moon, an Apollo liftoff, etc. YouTube is loaded with them. What evidence or
arguments could you use to counter this claim? Inform your students what the political environment was at the time. Given that
we were in a space race against the Russians, and given that they were spying endlessly on us, wouldn’t they have pounced
with glee on our failure to go to the Moon? Are we to expect that all the other nations part of the conspiracy? An excellent source
of arguments and counterarguments on this and other pseudoscience issues is www.badastronomy.com.

Clicker Questions
Please see the instructor resources at www.mhhe.com/griffith for a PowerPoint file of suggested clicker questions for this
chapter. Remember that personal response questions are a proven way to keep students engaged and thinking about the material
as class progresses.

Answers to Questions
Q1 No, centripetal acceleration is a change in direction, as in orbital motion.
Q2 a. The velocity of a body moving in a curve is continuously changing because of the change in direction even though
the speed is constant.
b. Yes. Any change in velocity is acceleration.
Q3 The car with the higher speed experiences a larger change in velocity. The change in velocity for a body moving in a
curved path at constant speed depends on the speed and the angle between the direction of the final and initial velocity
vectors. The car with the higher speed is taking the curve in a shorter interval of time.
Q4 The change in velocity is greater for the curve with the smaller radius. Since the distance and speed were the same for
both cases, it comes down to comparing rate of change in angular direction.
Q5 Because both the magnitude and direction of the ball’s velocity increase, the acceleration increases proportional to the
product of the two changes.
Q6 Path 3, in the direction of the tangent to point A. Neglecting gravity, the body would move in the direction it was moving
when the force disappeared, in accordance with the first law.
Q7 There is a force radially inward due to the tension in the string that supplies the centripetal force needed for this motion.
There is also the gravitational force due to Earth’s proximity.
Q8 Only if the twirling is done in a region of space not subject to gravitational force of any body. But of course in that case
‘horizontal’ is arbitrary. As long as there is a pull of gravity on the string, there will be a vertical component to the force.
Q9 a.

b. The direction of the net force is radially inward to the center of the curve.
Q10 Yes. Above some maximum speed there will not be sufficient friction (static) to provide the necessary centripetal force
for circular motion, and the car will slide. The maximum speed will depend on the nature of the surface and the radius of
curvature of the road.
Q11 Yes. Circular motion requires centripetal force. For the banked roadway, the normal reaction force of the road on the car
can provide a horizontal component yielding the correct centripetal force for a given speed. At this speed, no friction will
be required.

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Q12 For a body in a vertical circle there will be two contributions to the force acting on a body: its weight plus the tension in
the string. The vector sum of these forces must equal the mass times the constant value of the centripetal acceleration.
At the lowest point the tension is the greatest and equals the sum of the weight plus the mass times acceleration.
Q13 The rider’s weight (downward) is the largest force.
N

mg

Q14 Air bags. They provide a cushion between the rider and other objects in the car. The rider decelerates more
gradually involving a smaller force and less trauma.
Q15 No, according to Newton’s first law, an object in motion will stay in motion unless acted upon by a net force. In a head-
on collision the driver continues to move forward (until impact) in the absence of any force. The car does have a net
force applied to it, so it stops, but the driver continues to move forward.
Q16 Yes. Particularly in rollover accidents seat belts prevent the rider from being thrown from the vehicle.
Q17 The Copernican model assumed that the planets moved in simple orbits about the sun. The Ptolemaic model had to
assume a more complicated motion involving a planet moving in a small circle while the center of that circle moved in a
larger circle about the Earth.
Q18 In Ptolemy's view, everything revolved about the Earth. The Earth was stationary and the sun and stars revolved about
it, as well as the planets in their epicycles.
Q19 All objects around us are moving at the same speed, including the air. Hence, there is no sense of motion relative to our
surroundings.
Q20 Copernicus, like the ancient astronomers, believed that nature is perfect and that orbits should be circles, since these
are the most perfect curves. Although Kepler was a mystic also seeking perfection, he realized that the observational
data required the orbits to be ellipses rather than circles. He also realized that the orbital speed of a planet was not fixed
as it orbited the Sun, but instead increased when closer to the Sun.
Q21 The ellipse becomes less elongated as the foci are brought closer together and becomes a circle when the two focal
points coincide.
Q22 A planet in an elliptical orbit about the sun moves fastest when it is nearest the sun. This is because an equal area of the
ellipse is traversed in the same time interval at both aphelion and perihelion (as well as for points in between).
Q23 From Newton’s third law we know that the interaction of two masses results in equal but oppositely directed forces. But
because the mass of Earth is about 1/300000 the mass of the Sun, the Earth’s motion is changed more by this force.
Q24 There is a net gravitational force acting on the Earth. The sun exerts the largest force, the moon a lesser force, and the
more distant heavenly bodies much smaller forces.
Q25 There will be a net force acting on m2 toward m1. The third mass exerts a force of attraction to the right, but since it is
farther away, that force is less than the force exerted by m 1 to the left.
Q26 Since the gravitational force of attraction varies as 1/r2, doubling the distance between them will result in 1/4 of the original
force acting between them.
Q27 No. There are no stars between the Earth and the moon. (Maybe blinking lights of a passing jet? Or a satellite or
International Space Station?)
Q28 The new moon rises in the morning (when the sun rises) and sets at dusk (when the sun sets).
Q29 The first quarter moon rises and sets about six hours after the sun, while the third quarter moon rises and sets about six
hours before the sun. (Noon and midnight are the rising and setting times depending on lunar phase.)
Q30 New moon occurs when the moon passes between the Earth and the sun. Thus the side of the moon facing us is not
illuminated (except possibly by earthshine—the light originating from Earth being reflected by the moon).
Q31 Solar eclipses occur during the new moon and only when both sun and moon are aligned with the same lunar node.
Q32 Because centripetal force is holding it in orbit, it is not ‘standing still’. This centripetal force is a result of its acceleration
around Earth. It happens that its orbit takes the same amount of time as one diurnal rotation of Earth.
Q33 Kepler's third law applies to all satellite motion but in the case of satellites orbiting Earth the mass of the sun is replaced
by the mass of the Earth so that there is a different ratio of T2/r3.
Q34 Because the moon moves relative to the Earth it takes about 25 hours for the moon to return to the same point in the
sky, so there are two high tides every 25 hours.
Q35 The center of the Earth is closer to the Moon than the water at the far side of the Earth. Thus the center of the Earth is
subject to a greater influence from the Moon than is the water on the far side. In essence, the gravitational tug pulls Earth
away from the water on the Earth’s far side, creating a tidal bulge where the water was “left behind.”
Q36 No. The phenomenon of tides comes about because of the difference between the force acting on the water at the surface
and the force acting on the center of the rigid Earth.

Answers to Exercises
E1 45.0 m/s2
E2 11.43 m/s2
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E3 1m
E4 4 times
E5 1N
E6 a. 6.43 m/s2
b. 8,360 N
E7 a. 18.22 m/s2
b. 18.2 kN
E8 a. 6.4 m/s2
b. 384 N
E9 365 : 1
E10 180 N
E11 0.05 N
E12 5.86 x 10-5 N
E13 .56 N (4 times greater)
E14 35 lb
E15 300 lb
E16 a. 4:00 PM
b. 9:48 AM, 10:13 PM

Answers to Synthesis Problems

SP1 a. 26.67 m/s2
b. 5.34 N
c. 1.96 N
d. Instructor will show students.

SP2 a. 9.77 m/s

b. 6.82 m/s2
c. 239 N is the necessary force; Yes.
d. Weight = 343 N, so difference is 104 N
e. If the rider lets go of the safety bar the rider will fly out at a trajectory tangent to the ferris wheel’s rotation (parallel to
the ground). At that moment gravity will also accelerate the rider to the ground.
SP3 a. 10.4 m/s2
b. 9.375 kN
c. 8.82 kN
d. Diagram below; about 9.1 kN
e. 2363 N; No. It is not sufficient

15º

SP4 a. 19.6 m/s

b. 154 m/s2. Very large, more than 15 times the graviational acceleration
c. 9240 N (using unrounded numbers, 9253 N)
SP5 a. 3.53 x 1022 N
b. 2.01 x 1020 N
c. 175/1; no
d. 4.34 x 1020 N, Not much, but some. The sun’s force keeps the moon in its annual orbit about the sun as it moves
along with the Earth.
SP6 a. 7.5%
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b. The moon advances in its orbit by 13.2o/day while the Earth advances 1.0o/day for a net of 12.2o/day. In 27.3 days
the moon will have an apparent advance of 333o, so it is not yet a full moon.
c. The moon has 27o to go to full moon. This takes about 2.2 days more.

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