PHYSICS 161 EXAM III: Thursday December 04, :00 a.m.

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1 PHYS 6: Eam III Fall 003 PHYSICS 6 EXAM III: Thusda Decembe 04, 003 :00 a.m. Po. N. S. Chan. Please pn ou name and ene ou sea numbe o den ou and ou eamnaon. Suden s Pned Name: Recaon Secon Numbe: Sea Numbe:. The Unes has a naonall ecognzed Hono Code, admnseed b he Suden Hono Councl. The Suden Hono Councl poposed and he Unes Senae appoed an Hono Pledge. The Unes o Maland Hono Pledge eads: "I pledge on m hono ha I hae no gen o eceed an unauhozed asssance on hs assgnmen/eamnaon." Suden s Sgnaue (n nk please): Ths es consss o 4 pas, each woh 5 pons. The eam s pned on 8 pages and s o be compleed n 50 mnues. Please check ha ou hae a complee eam. In mos cases paal ced wll be gen, so show ou wok. I ou need addonal space use he eese sde o he shees, o ask o addonal pape. Some o he ollowng nomaon ma be useul n he eam. g 9.8 m/s SCORING TABLE (Each suden should check he addon o hs own scoe.) Poblem Pons. /(5). /(5) 3. /(5) 4. /(5) Toal /(00)

The Unes o Maland Hono Pledge eads: "I pledge on m hono ha I hae no gen o eceed an unauhozed asssance on hs assgnmen/eamnaon." Suden s Sgnaue (n nk please): Ths es consss o 4 pas, each woh 5 pons.

2 PHYS 6: Eam III Fall 003. A.00-kg objec (mass m) sldes o he gh on a suace hang a coecen o knec con µ k 0.50 (See Fg). The objec has a speed o 3.00 m/s when makes conac wh a lgh spng ha has a oce consan k 50.0 N/m. The objec comes o es ae he spng has been compessed a dsance d. The objec s hen oced owad he le b he spng and connues o moe n ha decon beond he spng s unseched poson. Fnall he objec comes o es a dsance D o he le o he unseched spng. a) (0 pons) Fnd a (quadac) equaon o d n ems o m, µ k, g, k and. b) (8 pons) Assume d m and, nd he speed a he un-seched poson when he objec s mong o he le. c) (7 pons) Assume d m and nd he dsance D whee he objec comes o es.

The objec s hen oced owad he le b he spng and connues o moe n ha decon beond he spng s unseched poson. Fnall he objec comes o es a dsance D o he le o he unseched spng.

3 PHYS 6: Eam III Fall 003. A spos ca aelng Noh a 30 m/s colldes head on wh a uck headng Souh a 5 m/s. The mass o he ca ncludng he de s,500 kg and he mass o he uck ncludng he de s 0,000 kg. Ae he collson he wo ehcles sck ogehe. a) (8 pons) Fnd he speed o he weckage. Is mong Noh o Souh? b) (5 pons) Wha s he mpulse appled o he uck due o he collson? c) (6 pons) Assume ha he mass o he uck de s 00 kg and ha he s beled n. Wha s he mpulse epeenced b he de due o he collson? I he collson lass 0. s, wha s he aeage oce epeenced b he de? d) (6 pons) Assume ha he mass o he spos ca de s 00 kg and ha he s beled n. Wha s he mpulse appled o he de due o he collson? I he collson lass 0. s, wha s he aeage oce epeenced b hs de? 3

Is mong Noh o Souh? b) (5 pons) Wha s he mpulse appled o he uck due o he collson? c) (6 pons) Assume ha he mass o he uck de s 00 kg and ha he s beled n.

4 PHYS 6: Eam III Fall Two blocks ae conneced b a sng o neglgble mass passng oe a pulle o adus 0.50 m and momen o nea I. The block on he conless nclne s mong up wh a consan acceleaon o.00 m/s. a) (4 pons) Wha s he angula acceleaon o he pulle? b) (6 pons) Wha s he angula eloc o he pulle ae has compleed 3 complee eoluons sang om es? c) (6 pons) Deemne T and T, he ensons n he wo pas o he sng. d) (5 pons) Wha s he oque appled o he pulle? e) (4 pons) Fnd he momen o nea o he pulle. 4

a) (4 pons) Wha s he angula acceleaon o he pulle?

5 PHYS 6: Eam III Fall Med bag a) (0 pons) A bowlng ball wh mass M, adus R, and a momen o nea o 5 MR s eleased om he op o an nclned plane o hegh H. A clndcal ng wh he same mass M, adus R, and wh a momen o nea MR s also eleased a he same me. Boh oll whou slppng. Use eneg mehods o nd he cene o mass eloc, V CM, o each objec when eaches he boom o he nclne. Epess ou esul n ems o R, H and he acceleaon due o ga, g. Whch objec eaches he boom s? b) A bllad ball mong a 5.00 m/s skes a saona ball o he same mass (each mass s kg). Ae he collson, he s ball moes a 4.33 m/s, a an angle o 30.0 wh espec o he ognal lne o moon.. (0 pons) Fnd he suck ball's eloc ae he collson.. (5 pons) Wha s he eloc o he cene o mass beoe he collson? 5

Use eneg mehods o nd he cene o mass eloc, V CM, o each objec when eaches he boom o he nclne. Epess ou esul n ems o R, H and he acceleaon due o ga, g. Whch objec eaches he boom s?

6 PHYS 6: Eam III Fall 003 Possbl useul nomaon Chape Dmensons [M], [L], [T] ρ M / V sg. gs. Chape a a. speed oal ds./me d d a d d a ( ) a a ( ) Chape 3 cos(θ ) sn(θ ) In dmensons: A A A C A B C A B B B B C A B C C C A A ˆ A ˆj A kˆ z C an θ and n 3d. usng un ecos: C B B ˆ B ˆj B kˆ A A A A ec. z z Chape 4 a a 0, g a c a a ( ) ec. a R sn(θ ) h sn ( θ ) g g d a a a ˆ θˆ d a a a c a 6

/me d d a d d a ( ) a a ( ) Chape 3 cos(θ ) sn(θ ) In dmensons: A A A C A B C A B B B B C A B C

7 PHYS 6: Eam III Fall 003 Chape 5 F ma w mg R s µ s R k µ k Chape 6 a c Chape 7 W F cos ϑ F W F d k ( ) K m Wne K K P W P F Chape 8 U g mg U s k E K U Wg ( U U W nc ( K U ) ( K U K U K U ) ) W con d m mg m mg d k Chape 9 p m mpulse I F I AV p m m m m m m cm M F m k F s F I du d Fd ) cm M MV dm eenal Ma cm cm p p oal ( m cm m m m 7

K U ) ( K U K U K U ) ) W con d m mg m mg d k Chape 9 p m mpulse I F I AV p m m m

8 PHYS 6: Eam III Fall 003 Chape 0 θ s ω dθ d α dω d ω ω α ω a α θ θ ( ω ω ) I m ω K I Fd P τω θ θ ω ω ω α ( θ θ ) α a I dm c τ τ Iα W Iω Iω ω K ω I CM M CM 8

Goals Rotational quantities as vectors. Math: Cross Product. Angular momentum

Goals Rotational quantities as vectors. Math: Cross Product. Angular momentum Physcs 106 Week 5 Torque and Angular Momentum as Vectors SJ 7thEd.: Chap 11.2 to 3 Rotatonal quanttes as vectors Cross product Torque expressed as a vector Angular momentum defned Angular momentum as a