Fal l20l3 PHY2318HW#1

1. A curve in a road forms part of a horizontal circle. As a car goes around it at constantspeed s1, the horizontal total force on the driver has magnitude Fr. What is the totalhorizontal force on the driver if the speed on the same curve is s2 instead?

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F , = r r r kW h u , S < S a , F - F z

q - z

F . = n ?r llt Sr"\s/w + *"-

,:'frl -1 rh S,L

E+ r,:(g', =(il!Pr W*br, F= H I"t m w'\^fQ **<".'-fz^,*

F <* ve

F'= (H) o,

* o

._@

Sr'5 r -

F*

21. I"the Bohr model of the hydrogen atom, an,electron moves in a circular path around aproton. The speed of the electron is v.(a) Find the force acting on the electron as it revolves in a circular orbit of radius R.(b) Find the centripetal acceleration of the electron.

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tt th'* ( IN"o "'bt'* L m '

Eq^al;^ $ rno[in-,r F=rn&. --O

a"=F *@,

@ + a- =# cA^^,^,u, w # ct)).

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F' *H C/+,", * [* fe h)),

F l\ /

(lrrr[ , F, tt^* y*Lh, ?oo, *-/ t" k,,r* t't" -1*M"t'tA^"o W= 4 .lO 7 Xt6-tf hf .)

3"r*. Determine the gravitational force that you exert on another person at a distance Laway. Assume that you and the other person are point masses of m each.

f n Fo+

r-c m.m r ' lnL' - = ( - t -

L L .(Ar"r,*,"1)

4,,fr. fwo objects allract each other with a gravitational force of magnitude F whenseparated by d. If the total mass of the two objects is M, what is the mass of each?

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F lltw@

k +U rn^,to ,+ ft*{'tro 6Lgdt L- y4' e"*L rh* '

F = G W + r f r , t y t , = W -'e

t f f i *H*$ F4n ,+ W =Q" -*- cx)}.,1 *Jf1"- +ry

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(L;gl*r^ , )Lna. *il"- ,-t),

f^. W v^"]rtw^jicio*,a: 0 Lww,go dQ v* ot."ft#- i:,.r*,^d^^tet,n*rCIp. vr, ao'sl 'vut t- ,,ffe lt r". taok *t cr), ff) ; tt**-**t {1r"t6*^LO ; Ws trrnr,l rDzlg.

YII ,tfh * ,- f''rl'hw tv"*b*Gu,;wr ( . r l r , & w(z)

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0+r , =W,S-t- ,'-+t Cg + rvtt

++

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I I r=

T^le, Ytt,= l4+Wtr:Mz

+U r/tu? 11 * ln t

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4 

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6. A force il lnri+ By?),where Fis in newtons andx andy areinmeters, acts on anobject as the object moves in the r direction from the origin to x: a . Find the workdone W =

I F.d?bythe force onthe object.

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{

drJ iAi " il*!,r

+ o

" d"(

.,. hJ = [+nf]:"

A

r 83 i

f . s

) F

*xiW eJp =

. ' . U\, 5 ct-l+ Bu t)' (a'l * &c A) '

J-fi" + f"t"-'*:0 -9'o

- | 1 - L= tft^':#

7. A block of mass m is released from rest at point @in the fieure below. The track isfrictionless except for the portion between points @and @, *]ri.tt has a length of Lmeters. The block travels down the track, hits a spring of force constant k, andcompresses the spring d from its equilibrium position before coming to rest momentarily.Determine the coefficient of kinetic friction between the block and the roush surfacebetween points @ana m.

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fila&,ar"J"+l* Et"l,',s daTV/ '

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^KE + A?E a du'[ ]i''@L! *-wv'a"/na*ive {.*g

+ (KE+-KE;)+(Wg-?E;) = wIvL 'l'nn-Ly non''*'uw''J"nfoe

/^ ftr* us t&O'

=!F !"

+ F,!, = Y^0,1^ * *l*At e N'""L* *,ot' \7

, '. (o *o)+ w ) +A P E f u , ̂Qtatt;{ationatr'"p'lu-/ri o)-

rIk"l'-o)t-.--fJ

^rE fuspi ,3

+ F A =g'* F = p*t

8. How much work is done by the Moon's gravitational field as a meteor of mass Mcomes in from outer space and impacts on the Moon's surface?

t,L , * - - t - 4

Cv=e7r/ao

Jtk W nLrrw dl tL "olruo'Lt ,n ,a'J Y\a.,p 4 t'1* L- l*4 t

udtl. A""* \ tL W'il;on*L [""a = -4U. _(04_ U; )

A\[un',Ku ,,CLod "

--(-Gw*o)=tG+f

-+ i (* tl p".:ht ).sF

-?r 4= m L Cr=e)

,'. gJ = [t E .Ai./;

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r Y"'^L 4 Y ^

^r

i).( lnF)"Jj,f: / Mrq ' In I- \{ ovlt-

(fr = il'')

9. A space probe is fired as a projectile from the Earth's surface with an initial speed ofv. What will its speed be when it is very far from the Earth? Ignore atmospheric frictionand the rotation of the Earth.

J"t tI* m'& ol Ltr*p'ie'f,ti Lu m '

vt8t1-c,r'rrw,anhve f-t' , *fTq co-anrva*;*'t{ ?*rffi:

CXeSt+ CPE); = C KEL tCPE)f .

,',. j+nv'* Gq: i *^vr" - GW;r

+ ! v ' - W s * V ' -

+ v+'-V"- W=) V*= zGY\".

Re

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No

M"tl;le ca,wn"t tvo"L tl*

, 6lirut,e'l,.- +l"b

F ; + ( Y = a ) -

10. At the Earth's surface, a projectile is launched straight up at a speed ofv. To whatheight will it rise? Ignore air resistance and the rotation of the Earth.

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',ls Yn 6/tra L n '

'(1^"A ta t'to tqfrrr-ca".aol,rtdnt'€' #'*

Gro*t"A"*.f- ry i

(kE> + l); e CKs)a + tft '

;.tvyrv,-GW = ln(o)'- Cry

zwFe

+ v'- = - W

f ty, Zt'FI"Ru'

2AHe' PeV t "

%t-1eKe *ReZGt4e- ReY'

*2

e Y ' P e =

frn*v'ZGHI - ReV "