practice+2b+solutions

# practice+2b+solutions - Physics 140 Fall 2010 Second...

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Physics 140, Fall 2010 Second Midterm Exam Physics Department, University of Michigan November 4, 2010 FORM 1 Please print your name: SAUL LOU SHEN Your INSTRUCTOR:_____________________ INSTRUCTIONS AND INFORMATION 1. Fill in YOUR NAME, INSTRUCTOR and the EXAM FORM NUMBER on the scantron. 2. RECORD YOUR ANSWERS ON THE SCANTRON USING A #2 PENCIL. 3. Turn in this exam copy with your scantron answer sheet. 4. This is a 90-minute, closed book exam. You may use two 3” x 5” card on which you have your favorite equations. You also may use a calculator but please do not share calculators. 5. All cell phones and other communication devices must be shut off and out of sight. 6. There are altogether 20 multiple choice questions. All questions are of equal value. Equations/values that you may find useful: s f = s i + v 0 t + ½ a t 2 θ f = θ in + ω t + ½ α t 2 Rod, axis through one end I =1/3ML 2 v f = v 0 + at ω f = ω 0 + α t Rod, axis through center: I = 1/12ML 2 a rad = v 2 /r v t = r ω , a t = r α Solid sphere: I = 2/5 MR 2 F = m a τ = r × F = d L /dt=I α Hollow sphere: I = 2/3 MR 2 W = F . s L = r × p = I ω Solid cylinder: I = ½ MR 2 F k = μ k N W = τ ( θ 2 θ 1 ) K Hollow cylinder I = ½M(R 1 2 +R 2 2 ) g = 9.8 m/s 2 U spring = ½ kx 2 Hoop: I = MR 2 F = −∇ U Impulse J = F .dt = Δ p I p = I cm + MR 2 W = Δ K P = Δ W/ Δ t = F.v K rot = ½ I ω 2 Δ K + Δ U = W n.c. in , 2 2 1 2 in , 1 2 1 2 1 f , 1 v m m m 2 v m m m m v + + + = in . 2 2 1 1 2 in , 1 2 1 1 f , 2 v m m m m v m m m 2 v + + + =

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Physics 140, Fall 2010, Midterm 2 Problem 1: A variable force (a force in the y-direction whose magnitude depends on the position) is acting on an object that is moving along the following path: (1) it starts at the origin and moves along the x-axis to a point x = 2m, y = 0; (2) it moves parallel to the y- axis to a point x = 2m, y = 3m; (3) it moves parallel to the x-axis to a point x = 0, y = 3m; (4) it moves parallel to the y-axis back to the origin. What is the total work done for the complete round trip? A. -12J B. 0 C. 12J D. 18J E. 27J Along A 0 0 0 = = = A W F y Along B 27 3 6 ˆ 6 2 3 0 2 3 0 = = = = = y ydy W j y F x A G J Along C 0 lar to pererndicu is = C W l d F G G Along D 0 0 0 = = = D W F x 27 = total W J. Answer E. Problem 2: Two bull frogs of mass 1kg and 2kg, respectively, sit at either end of a uniform narrow rectangular plate of mass 3kg and length 10m. The plate is at rest on the surface of a calm lake and has negligible friction with the water. The two frogs manage to trade ends without falling in the water. How far (in meters) does the plate move on the surface of the water? A. 0 B. 0.67 m C. 1.34 m D. 1.67 m E. 2.01 m Before After 1 kg 1 kg 2 kg 2 kg 3 kg 3 kg 5 m 10 m (0,0) (0,2) (2,3) (0,3) A B C D 3 F xyj = ± ±
From the left side of the plate before: 6 35 2 3 1 ) 10 ( 2 ) 5 ( 3 ) 0 ( 1 = + + + + = kg kg kg x CM m From the left side of the plate after: 6 25 2 3 1 ) 10 ( 1 ) 5 ( 3

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## This note was uploaded on 01/30/2012 for the course PHYS 140 taught by Professor Uher during the Winter '10 term at University of Michigan.

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practice+2b+solutions - Physics 140 Fall 2010 Second...

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