-
Notifications
You must be signed in to change notification settings - Fork 0
Expand file tree
/
Copy pathReadingGuide_Ch6_Solution.html
More file actions
368 lines (361 loc) · 15.8 KB
/
ReadingGuide_Ch6_Solution.html
File metadata and controls
368 lines (361 loc) · 15.8 KB
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
246
247
248
249
250
251
252
253
254
255
256
257
258
259
260
261
262
263
264
265
266
267
268
269
270
271
272
273
274
275
276
277
278
279
280
281
282
283
284
285
286
287
288
289
290
291
292
293
294
295
296
297
298
299
300
301
302
303
304
305
306
307
308
309
310
311
312
313
314
315
316
317
318
319
320
321
322
323
324
325
326
327
328
329
330
331
332
333
334
335
336
337
338
339
340
341
342
343
344
345
346
347
348
349
350
351
352
353
354
355
356
357
358
359
360
361
362
363
364
365
366
367
368
<?xml version="1.0" encoding="iso-8859-1"?>
<!DOCTYPE html PUBLIC "-//W3C//DTD XHTML 1.0 Transitional//EN"
"http://www.w3.org/TR/xhtml1/DTD/xhtml1-transitional.dtd">
<html xmlns="http://www.w3.org/1999/xhtml">
<head>
<meta http-equiv="content-type" content="text/html; charset=iso-8859-1" />
<title>ReadingGuide_Ch6_Solution</title>
<meta name="generator" content="Amaya, see http://www.w3.org/Amaya/" />
<link rel="stylesheet" href="vishidestyle.css" />
</head>
<body>
<h1>Chapter 6 – Applications of Newton’s Laws</h1>
<h3>Introduction</h3>
<ul>
<li>What forces are the focus of this chapter?
<ul id="ans">
<li>Friction and centripetal force</li>
</ul>
</li>
<li>What is an example of where these forces are important?
<ul id="ans">
<li>A race car travelling around a curve.</li>
</ul>
</li>
</ul>
<h3>6.1 Solving Problems with Newton’s Laws</h3>
<ul>
<li>Which 2 of the 5 steps problem solving strategy for applying
Newton’s laws are covered by the strategies for drawing the FBD from
the last Chapter? <span id="ans">2 and 3</span><!-- <li>Identify the physical principles involved by listing the givens and
the quantities to be calculated. Sketch the situation, using arrows to
represent all forces. Determine the system of interest. The result is a
free-body diagram that is essential to solving the problem. Apply
Newton’s second law to solve the problem. If necessary, apply
appropriate kinematic equations from the chapter on motion along a
straight line. Check the solution to see whether it is reasonable.</li>--></li>
<li>When the piano is being lifted to the second story window (See Figure
6.2), what is the system of interest? What are the forces acting on the
piano?
<ul id="ans">
<li>The system of interest is the piano. Tension pulling up and weight
pulling down.</li>
</ul>
</li>
<li>NOTE: if we know the system of interest in advance there is no need to
draw other forces which act on objects outside of the system (like F_T in
this example, which is dropped when drawing the FBD).
<p>-If a system accelerates purely horizontally, what is the magnitude of
the vertical acceleration component in the Newton’s second law
equation for the vertical direction? </p>
<ul id="ans">
<li>Zero.</li>
</ul>
</li>
<li>What is the difference between static and dynamic equilibrium?
<ul id="ans">
<li>Static – objects are at rest. Dynamic – objects in motion
without acceleration (ie constant v).</li>
</ul>
</li>
<li>Keep in mind that the pdf version of the book sometimes has odd spacing
in the text when vectors are involved. This is obvious in the equation near
the bottom of pdf page 270. The app, 1, and 2 are subscripts of the vector
F, not separate variables. The html version of the book does not have these
issues so if you think something looks weird in the pdf, check the online
version of the book, then ask your instructor. </li>
<li>Identify each problem solving step in Examples 6.1 – 6.5.</li>
<li>What is the direction do normal forces point?
<ul id="ans">
<li>Perpendicular to their surface.</li>
</ul>
</li>
<li>For Example 6.3 (What does the bathroom scale read in an elevator?), if a
person on a scale in an elevator and the elevator is accelerating downward
does the scale read a number less than or greater than the person’s
weight when the elevator is at rest? What does the scale say if the
magnitude of the elevator’s downward acceleration is g?
<ul id="ans">
<li>Less than, Zero.</li>
</ul>
</li>
<li>-In Example 6.4/6.5 the effect of the pulley causes two important effects
that are used in a wide variety of problems in this course: 1) The
rope/string to change direction as it bends around the pulley and 2)
because it is "massless, frictionless", is the tension in the rope on
either side of the rope, the same or different? <span id="ans">The
same</span>
<p>-Examples 6.4/6.5 also contain another very common occurrence in force
problems where one needs to solve for two unknowns with two equations, ie
solving two equations simultaneously. It is good to review the algebra
techniques for this again if they are still not fresh in your mind.</p>
<p>-Do the two equations in Examples 6.4/6.5 come from the fact that there
are two-dimensions or because there are two objects? <span id="ans">two
objects</span></p>
</li>
<li>-Understand Examples 6.6/6.7, It is sometimes necessary to combine
concepts from different chapters to find the net force. Which kinematic
variable from Chapter 3 and 4 needs calculated from the given velocities in
these examples before (or in addition to) performing the Force Problem
Solving Strategy
<p><span id="prob">-NOTE: TYPO in p. 278 (7/31/17 pdf) inExample 6.6 At the
beginning of the Strategy section: "We know that Δt = 2.00s and
(6.00i ^ + 12.00j ^ m/s) − (5.00j ^ m/s)" should be " We know that
Δt = 2.00s and <strong>Δv =</strong> (6.00i^+
12.00...".</span></p>
<p>-For Example 6.8 and 6.9, keep in mind that calculus is sometimes useful
when acceleration isn’t constant. <span id="prob">NOTE: We typically
do not cover non-constant forces in Physics 2051 until we introduce energy
(which is a more systematic way of dealing with non-constant forces,
amongst other things). </span></p>
<p></p>
</li>
</ul>
<h3>6.2 Friction</h3>
<ul>
<li>What is Friction?
<ul id="ans">
<li>Friction is a force that opposes relative motion between systems in
contact.</li>
</ul>
</li>
<li>What is static and kinetic friction?
<ul id="ans">
<li>static: two contacting surfaces are stationary relative to one
another (attempted movement). Kinetic: Surfaces are moving relative to
one another.</li>
</ul>
</li>
<li>When pushing a crate on a concrete floor and the crate doesn’t
move, are you pushing against kinetic or static friction? What friction are
you pushing against once the crate starts to move?
<ul id="ans">
<li>Static. Kinetic.</li>
</ul>
</li>
<li>Figure 6.10 shows a microscopic view of two surfaces. Friction arises in
part because of the ____________ of the surfaces in contact.
<ul id="ans">
<li>Roughness or any word meaning similar</li>
</ul>
</li>
<li>Which equation gives an expression constraining the magnitude of static
friction? Why does it have a less than or equal to sign?
<ul id="ans">
<li>Equation 6.1. Because the expression only gives the maximum magnitude
possible (μ<sub>s</sub>*NormForce). It is "usually" less.</li>
</ul>
</li>
<li><p>NOTE: "Usually" the magnitude of static friction is simply the minimum
needed to counteract any other forces acting in the problem, calculated by
Newton's 2nd Law considering all other forces in the problem: a "reaction"
force. </p>
<p></p>
<p>Which equation is for the magnitude of kinetic friction? </p>
<ul id="ans">
<li>Equation 6.2.</li>
</ul>
</li>
<li>Figure 6.11c shows the frictional force versus applied force. Why does
the curve rise linearly in the labeled "Static Region" ? <span id="ans">See
previous NOTE above. Because the static force is a reaction force: it
simply cancels any applied force so that Sum F = 0.</span>
<p>-Figure 6.11c: At small applied forces and above, is it mostly larger or
smaller than its value in the labeled "Kinetic Region" ? <span
id="ans">mostly smaller until it gets near the maximum. </span></p>
<p>-Figure 6.11c: . Why does the curve have a sharp peak? </p>
<ul id="ans">
<li>One answer: this is related to the less than or equal to sign in
Equation 6.1. See above.</li>
</ul>
</li>
<li>Table 6.1 contains common coefficients of friction. Given these values,
is the coefficient of static friction always larger than the coefficient of
kinetic friction?
<ul id="ans">
<li>Yes. </li>
</ul>
</li>
<li>In Example 6.10 (Static and Kinetic Friction), for each push force in
(a), (b), (c), and (d), does the box move? Why or why not?
<ul id="ans">
<li>(a), (b), (c) – no motion, push is less than static friction
force. (d) – it moves, the push overcomes the static friction
force.</li>
</ul>
</li>
<li>In Example 6.10 is (a), (b), (c) is the magnitude of static friction
given by fs = μ<sub>s</sub><sub></sub>F<sub>N</sub> ? <span id="ans">No,
because the maximum possible is not needed, so this formula is not used,
instead it equals what cancels/balances the applied force</span>
<p>In Example 6.11 (Downhill Skier), What component of the weight is equal
to the normal force? </p>
<ul id="ans">
<li>W_y.</li>
</ul>
</li>
<li>The trig relation sin x/cos x = tan x used after Example 6.11 is used
several times in this course.
<p>Why do surfaces feel warm when they are rubbed? </p>
<ul id="ans">
<li>Surface atoms adhere/ cause atomic lattices to vibrate, creating
sound waves generating heat.</li>
</ul>
</li>
<li>In Example 6.12 (Sliding Blocks), Why does the bottom block have two
separate friction forces acting on it?
<ul id="ans">
<li>From the top block and the bottom surface.</li>
</ul>
</li>
<li>In Example 6.13(a) and(b), does the crate slide? READING EXERCISE: What
is the crates acceleration relative to the bed of the truck?
<ul id="ans">
<li>(a) – No. (b) – yes. -2.06 m/s^2 ( =5-2.94)</li>
</ul>
</li>
</ul>
<h3>6.3 Centripetal Force </h3>
<ul>
<li><span id="comm">Tyler a lot of this stuff I added in this sectionis very
specific to how we teach the course in 2051 typically, probably not much in
here should you bother trying to "emulate"</span>
<p>-Notice the word "net" in the book's definition of centripetal force:
What is centripetal force according to the book: "Any net force providing
____________ ____________ motion?" What direction does it point? </p>
<ul id="ans">
<li>uniform circular. Toward the center of the circle.</li>
</ul>
</li>
<li>-NOTE: "Any net force..." means that centripetal force is just a
categorization for any group of forces, (summed in the net force sum), or
even just certain <em>components</em> of forces. Those which contribute to
the acceleration IN THE RADIAL direction during circular motion. Notice in
Example 6.16 (the 2nd example) it is only the horizontal component of the
normal force, not the whole normal force which is considered the
centripetal force.
<p>-NOTE: centripetal force (or acceleration) does not <em>only</em> apply
to only UNIFORM circular motion, but can also apply to accelerating
circular motion. </p>
<p>-In Example 6.15, which force or forces contribute to the centripetal
force? <span id="ans">(static friction only)</span></p>
<p>-Which equation gives centripetal force in terms of mass, velocity,
angular velocity, and radius of curvature? </p>
<ul id="ans">
<li>Equation 6.3.</li>
</ul>
</li>
<!-- <li>When a road is banked at a _________ angle, the _________ you can take
the curve.
<ul id="ans">
<li>Steeper. Faster.</li>
</ul>
</li> -->
<li>What must be true for ideal banking?
<ul id="ans">
<li>External force equals the horizontal centripetal force in the absence
of friction.</li>
</ul>
</li>
<li>Which equation gives the ideal banking angle?
<ul id="ans">
<li>Equation 6.4.</li>
</ul>
</li>
<li>-NOTE: Notice in Example 6.16 (the 2nd example) it is only the horizontal
component of the normal force (Nx), not the whole normal force which is
considered the centripetal force. If friction is present in that case it
would be the sum of Nx AND the horizontal component of the friction force
which would be categorized as the centripetal force.
<p>-When you turn right in a car, you move in a __________ line, but the
car moves ___________, you are not experiencing a force from the _________.
</p>
<ul id="ans">
<li>Straight. Right. Left.</li>
</ul>
</li>
<li>The car is an _______________ frame of reference because it is
accelerated to the side. The forced sensed by passengers is called an
__________ force.
<ul id="ans">
<li>Noninertial frame of reference. Inertial.</li>
</ul>
</li>
<li><span id="prob">NOTE: other books courses use the words "pseudo-forces"
and "apparent forces" meaning the same thing as "inertial force" defined
here--as well as "ficticious forces" which is used in the previous chapter
(but not in this chapter again) to mean the same thing.</span>
<p>-On a merry-go-round, passengers experience an inertial force that is
often referred to as a ____________force. </p>
<ul id="ans">
<li>Centrifugal.</li>
</ul>
</li>
<li>What scientific instrument uses the centrifugal force to hasten
sedimentation?
<ul id="ans">
<li>Centrifuge.</li>
</ul>
</li>
<li>The inertia of the particle carries sediment along what kind of path?
<ul id="ans">
<li>Tangent line.</li>
</ul>
</li>
<li style="background-color:#ffff00">What is the Coriolis force?
<ul id="ans">
<li>Inertial force causing the apparent deflection of moving objects when
viewed in a rotating frame of reference</li>
</ul>
</li>
<li style="background-color:#ffff00">What is an example of a system in which
the rotation of the earth must be considered?
<ul id="ans">
<li>Rotation of weather systems</li>
</ul>
</li>
<li style="background-color:#ffff00">Coriolis force causes hurricanes to
rotate in what direction in the northern hemisphere? What about the
southern hemisphere? This can be seen in Figure 6.28.
<ul id="ans">
<li>counterclockwise, clockwise.</li>
</ul>
</li>
<!-- <li>In an inertial frame, __________explains the path and no force is found
without an identifiable source.
<ul id="ans">
<li>Inertia.</li>
</ul>
</li>-->
</ul>
<h3>6.4 Drag Force and Terminal Speed</h3>
<ul>
<li>What is a drag force? What equation is it given by?
<ul id="ans">
<li>Force that always opposes the motion of an object in a fluid; unlike
simple friction, the drag force is proportional to some function of the
velocity of the object in that fluid. Equation 6.5.</li>
</ul>
</li>
<li>Table 6.2 has common drag coefficients.</li>
<li>What is terminal velocity? What equation is it given by?
<ul id="ans">
<li>Constant velocity achieved by a falling object, which occurs when the
weight of the object is balanced by the upward drag force. Equation at
the bottom of pdf pg 305. (NOT NUMBERED)</li>
</ul>
</li>
<li style="background-color:#ffff00">Which equation is Stokes’ Law?
When is it applicable?
<ul id="ans">
<li>Equation 6.6. If the object is small, slow, or in a denser medium
than air.</li>
</ul>
</li>
<li style="background-color:#ffff00">The equation at the top of pdf page 308
is Newton’s2nd law for the situation in Figure 6.33. Go through the
derivation of velocity and position of the situation in Figure 6.33.</li>
</ul>
<p></p>
</body>
</html>