Understanding Forces and Motion: Physics 8A Final Exam Guide
School
University of California, Berkeley**We aren't endorsed by this school
Course
PHYSICS 8A
Subject
Physics
Date
Dec 10, 2024
Pages
8
Uploaded by CountHornetPerson256
Name: _______________________ Student ID: _______________________ Section Number: _______________________ PHYSICS 8A FINAL EXAM SPRING 2024
1.(20 pts) Block A has mass mand block B has mass 2m. They are connected by a string of negligible mass. The surface is horizontal. Block B is pushed by a force of magnitude Fappat an angle 30° below the horizontal. It so happens that Fappand mare related by Fapp= 4mg, where gis the magnitude of the acceleration due to gravity. The coefficient of kinetic friction between block A and the surface is µ, and the coefficient of kinetic friction between B and the surface is µ/2. What are (a) the acceleration of the masses, and (b) the tension in the string? Your answers should be in terms of m, µ, and g(although you might not have all three of these in both answers). Also, you should use sin(30°) = 1/2and cos(30°) = √3/2. Fapp30°A B Initials:________ m 2m atFBP forAahÉTwatFBDforBFretNAMg0BMInamgfaMhaMmgIBwFaFartyMp2mgFapSir300NB2mg4mgI4mgFBTunisfu4mg2µmConsiderwholasystemnowtensionisinternalFretFaeso30ftFp3mAbnowforsoAFf4mgremImmg3maFnetaTfama2533mg3aTfatmaailfTgMmsmalgTmg
2.(15 pts) Block A, with mass mA, and block B, with mass mB, are on a horizontal, frictionless surface. Block B has an elastic spring with spring constant kattached to it. The blocks are pushed together, compressing the spring by a distance d, and released from rest. Find the speeds vAand vBof the blocks after block A is no longer in contact with the spring, expressed in terms of mA, mB, k, and d. vAvBInitials:________ A B A B wewereCombinemomentumandmechanicalenergyconservationPiPf0MPVBMAVAMIKitVKft VfOtKdIMAVAMpVpOMAVA'tImCMITVIEIMAmmVIImaIIVVAKaMaItmFfinintheoriginalequationsaresymmetricinAandBwecaninterchangeABandequationsarestilltrueWecangetUpbyswitchingsubscriptsUpKdMaCIIorwecouldderivethisalgebraically
3.(15 pts) A beam consists of two sections, each with a length of 3.0 m. Each section has a uniform mass density. Section A has a mass of 5.0 kg, and section B has a mass of 2.0 kg. A block of mass 6.0 kg is hanging from the point where sections A and B are joined together. The beam is attached to a hinge on the wall at its lower end. The beam is at a 50°angle with respect to the wall. A horizontal rope is joined to the wall at one end, and the upper end of the beam at the other end. Find the tension in the rope, and the magnitude and direction of the force exerted by the hinge on the beam. (Express the direction of the force as an angle counterclockwise from the +xdirection, which points toward the right.) B 50°hinge A Initials:_______ ChooseoriginathingeInetTattolloinIBIt405.0481198 4,4154sin50Hi6045169.84143.0lsin500viiiit2.04,79 fm s4L4.5n1si50TGonsin4001T67.2NFnetxHToHxTa67.2NFnetHyMatMolat Mpg0Hy50kgGOks2.0k98471274NHMAY1H144Ntan41.901062or6280242
4.(15 pts) Water is flowing through a horizontal pipe of diameter of 24.0 cm with a volume flowrateof 0.14 m3/s. It then travels up a vertical pipe of height 11.0 m. At the top of that pipe, the water is ejected horizontally into the air at just the right speed for it to land a horizontal distance of 10.0 m away from the vertical pipe. Find the pressure in the bottom, horizontal pipe. (You do not need to know the diameter of the vertical pipe. Note: The density of water is 1.00 x 103kg/m3, and 1 atm = 1.01 x 105Pa. Initials: _______ Firstfindthespeedwithwhichwaterexits thepipe04ViyOt490th11.0m0f9fms4otΔt1.50sY16.62msNowfindthepressureinthehorizontalpipeᵈAvId've0.14ms0.24mVV309msPIputpsyPIpupgyPPIpViv4pseyeY1.01105Pa1000Ksm6674F3.094141000ksm98484111.0m2.26105Pa
5.(15 pts) A string is L= 10.0 cm long, has a mass of 18.0 g, and is fixed at both ends. A standing wave on the string has an amplitude Asw= 0.20 cm. (This is the maximum displacement experienced at an antinode.) The left end of the string is at x= 0, and the first node over from the left end is located at x= 2.0 cm. The string is vibrating at a frequency of f= 300.0 Hz. (a) Draw the standing wave pattern, clearly showing the number of nodes and antinodes. (b) Find the tension in the string. (c) Find the maximum transverse speed vmaxof a point on the string at x= 1.5 cm. Initials: _______ ai.ieIEn.E101Ln54211104.0anVfFIFtµf045300.070.040mF25.9NetyeattAsiaKxcowtvycx.tl2WAsinthatsinwtAt1.5cmsinkxsin21sIsin3VymaxWAsinKx2nFAsinKx21T300.04711020ch270antson2.7mr
6.(20 pts) A monatomic ideal gas goes through the following cycle: (i) First it goes from A to B, which is a straight line in the diagram. (ii) It then expands from B to C, which is an adiabatic process. (iii) It is then compressed at constant temperature back to point A. The pressure, volume, and temperature at point A are P0, V0, and T0, and at point B the pressure and volume are 2P0and 2V0. (a)Find the temperature at point B, in terms of T0. (b)Find the volume at point C in terms of V0, and the pressure at C in terms of P0. (c) Find the work done by the gas and heat absorbed by the gas during each part of the cycle, in terms of P0and V0B P A C V Initials: _______ atPAYIIfIf2y161TVptToVpEFE1IE4421348Uc208IV164PAVAPVPVP16VIPP27A1BWareaundercurveIPatPKVValfP2PaIVV07IWPovIIT.tnNR4TT7EnRTPovo
Extra space for problem 6: Initials: _______ Ef.itBcIQ0sinceit's adiabatic45ItznrCTTHMRTo47InRTWIPVCIAWnorthVfP.V.tntoIPoV.G16orWYPowla2QWP.V.hnIT