Physics 1230 - Test 1 Study Sheet and Comments
Today's date: Friday September 22, 2013
Lecture Supplement No.5
Your first physics test of the school year will be held Monday September 25,2013 during our
regular classroom period. I'll try to get us started 5 minutes early, and I'll also try to squeeze out
an extra 5 minutes after class for those of you who are a little slower. But, this is officially a onehour test starting at 11:30 AM.
'
I've put together a little study sheet for you that may help you. The first two pages are review
(summary) sheets. The remaining pages are test problems (and solutions) from previous years.
The suggested study procedure is to FIRST study the lecture notes, text, quizzes and problem
sets. Then, take the exam just like you were taking the test on Monday. Finish the one test, and
then compare your procedure and answers to that on my solutions sheet. Then do the second.
Good luck everyone.
Jerry
Chapter 1
A. Know fundamental indefinables of physics: length; mass, and time. Carry along units in
calculations. Know the basic prefixes: ll, m, C, k, M. Know how to apply unit vectors i,
j, k.
B.· Know how to add vectors. You should be able to distinguish a vector from a scalar. Two
pieces of information are necessary to specifY a vector in a plane: (1) the magnitude of
the vector and the angle OR (2) two components of the vector.
1. Graphical (See Lecture Supplement No.1)
a. Parallelogram Method
b. Head-to-tail
(or polygon) method
b. By rectangular
resolution
A-/"
.
-"
.....
- n (.6;) C\.
2. Analytical Methods 8
R
11 _
a. By law of cosines & sines (seldom used)
_
B:.: - 5 ~ P,
l/r /?J
J%.ifJX
. 7h..-I'IR~~R:TRy"
6 7 if!
q.
f)~tf:N'!i
.
C. Newton's First Law tells us tEat if a body re~ins at rest or moves in a straight line
F", "" 0, L~ = or
with constant speed, then R = 0 (Equilibrium exists!) and
translational ecJ.uilil2ril.illl.. ­
Newton's Third Law tells us that whenever one body exerts a force on another, the
second always exerts on the first a force which is equal in magnitude but opposite in
. direction to the first. These forces are in pairs and always act on two different objects.
G:' Free Body Diagram. An object will undergo motion (or remain at rest) dependent upon
only those forces that are in contact with it and the weight forc~ (the one non-contact
force for each object that has mass where w =mg). In order to isolate an object, some
forces are given directly. Others can be determined from the following chart:
o
k
)?tl/(y
Rx
5:'
,:Ptt't ~'!5~i -ihi2jJ,Q~ }~~6s7t.
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:r=.
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CHlrP- 2,3 t -1, S,
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lSI
Help: SOHCAHTOA
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and
I EST
w = mg (where 9 = 32 ftls2 or 9.8 mls2)
1. Here are some quick questions to get the old pencil going:
(a) (2) Two microseconds, or 2 jJs, is _1_ S
s
(b) (3) A mass of 20 kg will wejgh _7_ N
N
(c) (3) Identify the reFlction force to the weight force-i.e., the force exerted by the earth on an object:
2. (a) Poor Jasper lost his dog Jack both starting at the origin. Suppose that Jack strays 25 ft Wand
then 50 ft at 30° N of W. But then Jasper initially walks 75 ft at 45° S of E and then 100 ft at 3~ W of
S. (i) (3) Draw a vector diagram approximately to scale illustrating both Jasper's and Jack\s paths.
(Ii) (12) How far away and in what direction
"BON
must Jasper walk in order to directly run in to Jack?
501'1
bO·· .
20t,J
(b) (10 pts) Find the resultant (magnitude and
direction) of all five forces on the illustrated FBD:
T
I,OOM
o
!
40';
30';
r- ;SZ>1II~
r
-.Y/.
3. (30) Given the 100 N weight on the 37° (below left). The string T1 is run parallel to the inclined plane and is attached to a knot as shown. If the coefficient of static friction is 0.50, find the weight W (largest value) which will allow the system to remain in equilibrium. Also find T2, T 3 , and T4 • (Yes, that is the same rope that is wrapped around the pulley.) Ii.
../jJ,
fLo 0Lcl11
#-1­
B
-r;
f---"":"---tr'
A
4. (30) In the diagram above to the right, block A weighs 200 N and is pulled to the left at constant
speed by a rope directed over a pulley to an unknown hanging weight W. As it is pulled, block B
weighing 40 N slides over the top~ of block A and is held in position by a set of three ropes T 1• T 2 ,
and To tied in a knot.Ttie coefficient of sliding friction between all surfaces is 0.25. (a) Find the
weight W. (b) Find the tension in ropes Tj, Tz, and T3 . As usual, draw the FBDs, and next to each
diagram write the appropriate equilibrium equations.
5. (20) A 100 N steel block is being pulled at constant speed over a steel surface. From our text
book. one obtains I-lK 0.57 and J.ls = 0.74 for the coefficients of kinetic and static friction
.
=
respectively. Find the force F that makes an angle of 3~ with respect to the horizontal that is
npr.pc;c;J:l1V tn J:lr.r.nmnlic;h thic;
~nrl
J
r
~
Sled
r_
finti thp frir.tinnJ:lI fnrr.p :.:anti thp nnrmJ:lI frirr.p
1
370
5/7
F6 V
h
OP- 'F-N CJ'I
T,,/~
T
<
..
/~
T3
~FIlC ~o
-
~
+
(Of) /II t- It ..c...(.~ J 1_1:'-...:;;.-_-......
,;:..(.c-)':.oIOCNqJ i't,r:.1('7tJ
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T'~ (..,lJ) 37"- T~ ::' 0
/. '::;..f.{~ 7N)C.~)
C.+:!> :. 13 41J"-J E.Y
F@
J P>c. \':'...
-'2.~1
~
$t)1
),rl~
OF 'P1J1.1.,6 Y
T'i' ::' T", :. I 3 <t ;J
-.r.-<.c........p
l-F,/"::.O ti­
- C.s'
p,.,. Nt
t- so'''';'' 1.0°
:::- t-ts'
f34N-iV~'O
@ =- elt<,(~
@
2 'JP '{EsT
Help: SOHCAHTOA
and
w
Fo12-~7fTC TreE-" =mg (where 9 =32 ftls" or 9.8 m/s-)
1 Here are some qUick questions to get the old penC-il gOing:
Q) A hand pushes on a book causing it to stide and accelerate aemss a horizonta11able,
{a) (2) MtJltipie Choice: The force -exerted by the hand 'On the book 15 {less than,equai to,
greater than) the force exerted by the book on the hand. (Chooseone.)
(b) (2) Your answer to part a 1S based upon which one of Newton's three laws?
(ii) (3) For projectile motion, constant acceleration of 9.8 m/s2 occurs in the _?_ direction, _ _ constant velocity occurs in the _?_ direction, and the slope of the Vy versus t graph gives _?_. 2. Jasper and Jezebelcontinue their rather bizarre relationship! Jezebel takes off in her Hummer initially at 400 m in front of Jasper and moving .at a constant speed of 20 m/s. Jasper, spotting Jezebel, floors the acceierator of his classy, energy-saving electric vehicle beginning initially at rest and accelerating at 0.50 m/s2 in an attempt to catch his wonderful Jezebel. (a) (20) Find the time it takes for Jasper to catch Jezebel, how fast is he moving when he overtakes her, and how far does he have to travel? (b) (10) Include acceleration vs. time, velocity vs. time, and dispiacement vs. time graphs for both Jasper and Jezebel. 3. Carlos Delgado, in the fourth game of the Mets/Cardinals NLCS, hit a towering three-run homer. Assume that the baJJ left his bat at an angle of 53° and a speed of 80 milH where 88 ftls 60 mi/H. Assume that Carlos hit the ball at 5.0 ft above the grpund and that the wall is 335 ft from home plate and 20 ft high. (a) (6) Write down the acceleration, velocity, and displacement equations for both the horizontal and vertical motion. (b) (9) How high was the ball above the wall as it passed over it. (c) (9) Find the magnitude and direction of the velocity vector of the ball as it passed over the wall. (d) (6) Include acceleration vs, time, velocity vs. time, and displacement vs. time graphs for both horizontal and vertical directions. =
4. (a) (15) Jezebel took up flying lessons. Suppose that she pointed her plane due north with an airspeed of 225 km/H but ended up, after 1.50 H, at a position of 250 km north and 50 km east of her initial position. Find the magnitude and direction of the wind velocity relative to the earth. (b) (15) Jasper, weighing 70 kg. decided to test the laws of physics on his own. Suppose that
he took off with bathroom scale in hand to the local Ferris wheel. Suppose that the radius of the
Ferris.wheel is 44 m and that it takest9.0 s in oroerto make one complete revolution. (i) Find the
centripetal acceleration of the Ferris wheel. .(ii) If Jasper sat on the bathroom scale, what will its
reading be in N at the very bottom of the wheel. (iii) What will its reading be in N at the very top
of the wheel?
5. In the diagram, all pulleys are light and
frictionless. In the diagram shown,
(
(a) (15) find the tension in all ropes,
(b) (10) find the acceleration of each block, and
(c) (5) find the time that it takes for the 5.0 kg
block to hit the floor if it starts from rest.
R
For:
ax 2 + bx + cO,
-b±,Jb2 -4ac
Get: x = - - - - - ­
2a
h1A-::5~
A
(j
2.C>l"\ Ih
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