Physics Sp Exam #4 Name:

Transcription

1 Phyic Sp. 017 Ea #4 Nae: 1) A coputer hard dik tart ro ret. It peed up with contant angular acceleration until it ha an angular peed o 700 rp. I it coplete 150 revolution while peeding up, what i it angular acceleration? Thi i jut a contant angular acceleration proble with 0 150rev 94.5, i 0, and rev rev in Uing the contant acceleration in rev 60 equation: ( ) i i (94.5 0) 301 ) A olid phere o a 5 kg i rolling without lipping with total kinetic energy 7 J. With what peed i a point on the top o the phere intantaneouly oving? The energy o the rolling phere i jut given by the u o the linear and rotational kinetic energy: 1 1 KETot KElin KErot v I 7J and given the relationhip between the rolling and linear velocitie: 1 1 v 7J 5kg v 5kg R 5 R 5kg kg v v 7kg 7J v v 1.4 i the peed o the center o a. But the top o the phere i oving twice thi peed, o v=.8/. i,

2 3) A thin, unior 4 kg rod, 1 long, ha two very all (point particle) ball glued at either end, one with a.5 kg and one with a 3.5 kg. It i upported horiontally by a thin, horiontal, rictionle ale paing through it center and perpendicular to the bar. At the intant hown, what i the angular acceleration o the bar? 3.50 Thi i jut a rotational Newton' Second Law proble: I The oent o inertia o the object i the u o the oent o inertia o the contituent, o I I I I.5kg 3.5kg bar 1.5kg kg kg kg The weight o the bar create no torque about the ael ince the ael pae through the CM o the rod, o:.5kg kg kg.67

3 4) A circular hoop o a, iu r, and ininiteial thickne roll without lipping down a rap inclined at an angle θ with the horiontal. What i the acceleration a o the center o the hoop? The orce on the hoop are the weight and the orce o riction, o applying Newton' econd law: F g in F a. Neither the orce o riction nor the acceleration i known, o we ut look at rotational otion: a F r I r r F a Putting thi into the irt equation yield: g in a a a 1 g in 5) What i the iniu coeicient o riction μin needed or the hoop to roll without lipping? In the cae o the iniu coeicient o tatic riction, F FN, o we ut analye the y-coponent o the orce: Fy FN g co 0 FN g co. So, F F g co N F g co but ro the irt proble, 1 F g in 1 tan g co g co

4 A diver o weight 775 N tand at the end o a 4.5 diving board o negligible a. The board i attached to two pedetal 1.5 apart (circled below). 6) What are the agnitude and direction o the orce on the board ro the let pedetal? Newton econd law or rotation tate that the u o all the torque will be ero or a tatic equilibriu ituation. Setting the pivot point at the right upport, we have Fl * N*3 = 0 or Fl = 1550N downward. 7) What are the agnitude and direction o the orce on the board ro the right pedetal? Newton econd law or a tatic equilibriu ituation ay that the u o all orce ut be ero or -775N 1550N + Fr = 0 or Fr = 35N upward.

5 You open a retaurant and hope to entice cutoer by hanging out a ign. The unior horiontal bea upporting the ign i 1.60 long, ha a a o 16.0 kg, and i hinged to the wall. The ign itel i unior with a a o 3.0 kg and overall length o 1.0. The two wire upporting the ign are each 37.0 c long, are 90.0 c apart, and are equally paced ro the iddle o the ign. The cable upporting the bea i.10 long. 8) What iniu tenion ut your cable be able to upport without having your ign coe crahing down? Another equilibriu proble, o the u o all torque and orce ut be ero. Start with the torque about the pivot point o the hinge (ince we know nothing about thoe orce): kg kg kg F in co 0 Cable N N F 0 F Cable 469.N Cable

6 9) A erry-go-round with a iu o and a oent o inertia 100kg i rotating at 0. revolution per econd. A child o a 50kg run at the erry-go-round in a line tangent to it edge, and grab onto it. Ater the child i on board, it rotate at 0.3 revolution per econd. How at wa the child running? Thi involve conervation o angular oentu, L I r p i i errygoround child rev kg kg v rev L Ierrygoround I child rev 100kg 50kg 0.3 rev Solving or v, we get v=4.4/ L i L.

7 10) A yte o two paint bucket connected by a lightweight rope i releaed ro ret with the 1.0 kg bucket.00 above the loor. The pulley ha iu and a oent o inertia kg. The rope doe not lip on the pulley ri. During the tie that the 1.0 kg bucket drop to the loor, riction in the pulley reove 10.0 J o energy ro the yte. What i the peed o the bucket when it hit the loor? Fro conervation o energy, the net change in echanical energy i the work done by riction, o E W K U U ech k g el 4 J v v 0 1 v 1 v 0 1 I 1 I kg 1 kg 4kg 1kg Pulley 4kg 1kg 10J 1 v 1 v 1 I gy gy Pulley 4kg 1kg 4kg 1kg v 10J 1 v 1 v 1 I gy gy r Pulley gy g y 4kg g y 0 0 v 10J 1 1kg 4kg v kg 4kg g 1kg g 0.16 v 10J 8kg 4kg kg 15.4kg 15.4kg v 9.5 v 3.08