Online Homework 5 Solutions

# Online Homework 5 Solutions - Pulley and Two Masses A...

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Unformatted text preview: Pulley and Two Masses A cartofmass M1= IS kg is attached to abluck ufmassM: = 3 kﬂhy a string thntpasses over a ﬁ'icﬁonlcss pulley. Tha system is iJ:Ii1:ia]I},Ir at roast and the table is ﬁ'ictiunlws. After Lhe block has fachn a distance I3. ==r l 111: What is the wad: W. dune an the cart hy'the string? 0'1. Black en Spring without Frictien i _:_ Final displacement giiilllllllltlltttltlllm I | -:- Inl-tlel dlepleeenmt A spring is stretched a distance efdx= Ill} cm beyond its relaxed length. Attached tn the end of the spring is an hlcck cf mass m == 1!] kg, which rests en a herizentnl ﬁ'ictienlces surface. A three cf magnitude 25 N is required to hold the block at this pesitinn. The force is then removed. a} When] the spring again returns to its unettctched length, what is the speed cf the attached object? ' b) When the spring has returned only hsiﬁsrsy (26* em}. what is the speed cf the attached object? ltd): : 95“ Oﬂm é k(—G—x>1+ Lm Block, Inclined Plane, and Spring An object ofmsss M = 3 kg slides frem rest a distance d - I In down a ﬁ'ictiernlesn inclined plane where it enootmters a spring. It eompresses the spring a distance I} = 1.5 in before stopping. The inclined plane makes an angle {-l = 30° with the herizentsl. a) Wilﬁl'l the hloek just touches the spring; how much gravitational potential energy has it lost? Give your answer use positive nmnher. b) After the mass has ﬁllly enmpressed the spring, what is its total loss of gravitational potential energy? Give your answer as a positive number. e] What is the value ofﬁie spring constant? Lao beam WW I. ”L ELLE) : 52.0IU 1L 3 1(51fﬂ) : P—ﬂ “-6002 w Loop-the-Leop [a] (bi '0 = 0. Ll-me) The two problems helps.r are related to a eart ofrnass M = Sill} kg going around a circular ieep-the—loep of radius R = 5 or, as shown in the ﬁgures. All surfaces are frictionless. In order for the cart to negotiate the leap safety, the normal three exerted by the traek en the can at the top of the loop must he at least equal to 0.4 times the weight of the earl. You may neglect the size of the cart. (Note: This is different from the conditions needed to "just negotiate'I the loop.) a] For this part, the amt slides down a ﬁietienlese track before eneeantering the loop. What is the minimum height h above the top of the loop that the eart can he released from rest in order that it safer negotiate the loop? h] Fer this part, we launch the earl horizontally along a surface at the same height as the bottom of the loop by releasing it from test them a compressed spring with spring eonstant'lt = Itltltltl Him. What is the minimum amount X that the spring must he enmpressed in order that the eart “safely“ (as deﬁned above} negotiate the loop? e) When the ear is descending vertically [in at a height R above the ground) in the loop, what is its speed M? d) At the bottom efthe loop, on the ﬂat part of the tree}:1 the sort must he stopped in a distanee ofd = II} In. What retarding aeeeleration III is required? . 'L. 595 “‘5‘” = if.“ {L M t Nuns = WE will“ Milling m?) /' \_ a}: 20% vi”: liq—3F— 1'11 4442} in: 0.111, = 35m Bnhslcd ftictien is negligible. Between points D and E at the end ct“ the run. the cccfﬁcient cf kinetic ﬁicticrn in nu - [1.4. The meat: ci‘thc hchcled with dtivers is 11!} kg and it stints 'ﬁtzttn restat point A. Find the distance it heynnd paint [it at which the bcheled will cctnc to a halt. Wendi Wim- "EH : main MIL 1n: E301 E‘ﬁmﬂ repaint = t“? Wm ch = —-‘xﬁ_ 7- -—‘><f4umoh’ 0* L1: wN/(Firfmj, ><= in : 50m : F 1:33.} [11?” '—'-'—l-—'———'r—" 1 "' "__" ' ' Block on Spring with Friction A relaxed spring with spring constant k= on Him is stretched :1 distance d; - Ti] cm and held time. A. block of mass M = 5| kg is attached to the spring. The spring is then released from rest and contracts, dragging the hie-ck across a rough horizontal ﬂoor until it stops without passing ﬂujough the relaxed position, at which point the spring is stretched by an amount dr= dJB. What is the coefﬁcient of kinetic ﬁictiorn pk hetwcm the block and the floor? ‘aWi M: (3%; Meme 9“: ic(cif+ci1i: (mN/m)(%+§)i& m @ _____._————---—_——_' (101% 20:: 1496'; W79) ...
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