Physics 122 Exam #1 Spring 2015

You are subject to the Bryn Mawr College honor code while taking this exam. This is a closed book exam. You may use a simple calculator and a pencil during this exam, but nothing else. Do all questions on the exam. Do all work directly on the examination, in the space provided. If you run out of room, you may use the back of the page. Be sure to answer all parts of each question. Some problems will take longer than others, but all will be weighted equally when graded. When providing a sketch, please be as neat, accurate, and quantitative as possible. A sloppy sketch indicates misunderstanding and will receive a reduced grade. The final page of this exam provide several potentially useful equations. You may remove this page for easy reference.

This exam will be available between Friday, 27 February 2015 and Mon­day, 2 March 2015, at the reserve desk in the Collier Science Library during normal library operating hours. I will collect all of the exams Tuesday morn­ing when the library opens. Take the exam during a single 90 minute sitting in the library.

Before you begin, write your name in the space below and at the top of EVERY page of this exam, note the date in the space provided on this page, and note the time. When you finish, note the time and return the exam to the circulation desk. The difference between your start and finish times should be no more that 90 minutes.

Name:

Date:

Start time:

Finish time:

1. For the swinging pendulum shown below, (a) make a diagram indicating the acceleration of the bob at positions P (the end of the swing) and Q (the bottom of the swing), and (b) draw force diagrams of the bob when it is at positions P and Q, In each force diagram, show both the individual forces as well as the net (resultant) force, if any, acting on the bob, (As a more familiar example think of a child on a playground swing.)

/

p " --- ... ---Q

Tile speed is momentarily zero a( point P The speed is IIO( z('ro at point Q so t horo so there is 110 radial uccclcrutiou. Howeve-r. uiust h(' rudial component of 1\('cdf'l'I.llion, there is n force acting t Hrt_(!;vlltialJ,v, which Howe-ver. no Ion ('S net i 1\1 1)2;C'1l I ial lv so i h('r(' eLLI\tlge's t 1'1<' spced ;,t( t llis point (I he' hoh is no t ClllP;<'1 II if" ac('clem t ion. doesn't remain sf ()PIH'd),

rnd in I o

a

(HaiS<'1l1 ia]

tangential

radial

radial

FOIl

t illlg('llt in]

."" " " tangcut ial

Fe; = Illy Fc = my

L

2. A ball is thrown at an angle e up to the top of a cliff of hieght L, from a distance L from the base as shown below. Find an expression for the speed necessary to make the ball hit right at the edge of the cliff. Your answer should only include the quantities given, Land e and known constants such as g.

,,, "x! "/ 'XI> f ~~ t , ,,

,

L: ~ I- Vo (__(/)._f) f L

_sJ::__ [ 2- ( , o (

3, Two stones are released from rest at a certain height, one after the other. ( a) Will the difference in their speeds increase, decrease, or stay the same? (b) Will their separation distance increase, decrease, or stay the same? (c) Will the time interval between the instants at which they hit the ground be smaller than, equal to, or larger than the time interval between the instants of their release? Explain your reasoning in each case,

, /P't

5f(~4s w//I .sl-~y 1-~5~ ~{ ;-k'j It'.{ /1. 1k d;, /' ~;~I1("( ; y.. .:>;>r: cd; /5 -;)Z (> t-1J Y1 j Y f~

.I::- Vr:.rft'cJ /IV?~J "t~1-1A./ e~rL rv t-w ~ 5 r/-rc.,!J .4 /-- //rl r:' ~

/"'" jL V-t- LUYI/Y7_

A J ftrntttf/I/I-L /7) w-<.. ~ ~/d ~ a bt r: ?(IV1 J./~ J- <1u L J~/,,~//Yl

/(/I\.l. f,,/l. ,~o/?< ' c ~F ~ 'VYl4 ~ bI--

.> I-~ / ~ Y\t.I<~r/( tJt f ti~ i;e/'o ~..J .>I-C/V'J- '2- J f"~ I" TLA ~~ ~/cJt/-/7~I .e a -: /-.,_ d->~ IJ't'r .)-/~ /5 . V'; to - J t ~,,( 1r). "- - J (t - T) . rl...- / r: vi / .(' 1'6\ ~ ce I 5 '1/;2.. - "VI -=-:) T ) wA /c 4. /) /V}~~f c:/ rl'~ ~ u: 70 /r- .5.~I' Pvl a 1/ h?

.;1u_ (I-M hi (J I /~ Iv?61' or M t''J k/~/V\~'c.> J X { ~ ~ J (-7.. PVVL~<-

'X'1_;:: ~~j (It-T)"L . Sa Xz -)I, ~ JtT f-~JT~ tu}vic,f.. ;' J1. t.~~ I/LJ; -?h t-)~ 6 _ (') rL +/A-L- ;~~r V'tt/' (pIli Pe ~.5q ~

tts 5~ /1-.... kL x~ t (~V< C'{6V'1/"-f'.

4. An object of mass 7nl attached to a spring of force constant k slides on a frictionless horizontal surface. It oscillates with an amplitude A. When the spring is at its greatest extension and the mass, 7nl, is instantaneously at rest, a second object of mass m2 is placed on top of the original mass. What is the smallest value that the coefficient of static friction can have if the second object is not to slip on the first? Explain how the amplitude, angular frequency and period of the oscillating system are changed by placing 7n2 on 7n1.

r-s a(-~l

~lS -=- ~ f T-VVl'__) (A_ ® F-s - ~ c M vC___ ® -s- ::: tvl pO-

(j) ~ A z: (M, +- VVt._,) a: lA- s- ::;. M"tA..

S ~ rK- ~ fo f a.. &f/f\~ (J d- ) Yv' fo (j) a.= -:f/ VV1 '2-

~ A t:. ~ I +--fVl1_ \ -t/v~ ~ J ~AN =)A-V"ILd f._. A -z (1M I rvVI.,J »<: J~

;{.A

Potentially useful equations

Vx = vox + axt x = Xo + voxt + ~axt2 v; = v6x + 2ax(x - xo)

r = rr v = if + ref} a = U - r(J2)f + (re + 27~(J){J

v2 ac = - = W2T

r V = rw

27f W = 27fJ = -T

F=ma Fjriction = f-lN VV = mg

F, = -kx F _ GMaNh

grav - r2

for q + w2q = 0, q(t) = A sin(wt + ¢)

A . B = I A II B I cos e A . B = AxBr + AyBy + AzBz IA x BI = IAIIBI sin e A x B = i(AyBz - AzBy) - j(AxBz - AzBx) + k(AxBy - AyBx)

9 = 10 m/s2 G = 6.673 X 10-11 m3kg-1s-2

-b ± Jb2 - 4ac for ax2 + bx + c = 0, x=------

2a