PHY131_F02_Midterm2A_solutions

# PHY131_F02_Midterm2A_solutions - Midterm 2 1 Nov 5 2002...

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Midterm 2 1 Nov 5, 2002 PHY131 Midterm Exam II Name/ID:________________ ________ Section:______ SOLUTIONS Vs. A – November 5, 2002 Prob 1 Prob 2 Prob 3 Prob 4 TOTAL 3 × OK: 4 × OK: 1.5 × NOK: 2 × NOK: NET: NET: Max. 29 points Max. 30 points (Out of 90) Formulae: Work done by a force F over a trajectory: W F d x Examples of forces: Force of Gravity (on mass m near sealevel) F G = mg (– j ) (downwards) ( g = GM E / R E 2 = 9.8 m/s 2 ) Force of Gravity (between masses M and m ): F G = ( GMm/r 2 )(– r ) (attractive) ± Force of a spring (spring constant k ): F S = – k x (opposes displacement x ) Rocket Thrust: F T = – v gas dm / dt Friction: F f = µ N (opposes motion) ( =coef. of friction; N =normal force) Kinetic Energy K : K ½ mv 2 Work-Kinetic Energy relationship (using Σ F i = m a ) Σ W i = K K f K i Potential Energy due to a conservative force F : U F U f U i = –W F Potential Energy of Gravity (mass m near sea level): U = mgy ( U ( y= 0) = 0) Potential Energy of Gravity (of masses M and m ): U = – GMm / r ( U ( r= ) = 0) Potential Energy of a spring (spring constant k ): U = ½ kx 2 ( U ( x= 0) = 0) Mechanical Energy E : E K + Σ U i Work-Energy relationship: ( W NC : work by non-conservative forces) W NC = E E f E i Momentum p of mass m with velocity v : p m v Force and its consequences: Σ F i = m a = d p/ dt J ∫Σ F i dt = p p f – p i Conservation of Momentum if ( Σ F i ) ext = 0 p i = p f Angle θ (in radians): s (=arc length) /R Angular velocity ω ; angular acceleration α : v TAN /R ; a TAN /R Rotational Kinematics for CONSTANT : = 0 + t; = 0 + 0 t + ½ t 2 ; 2 = 0 2 + 2 ( 0 ) Torque τ by a force F attaching at a distance R from a rotation axis τ R × F (vector product): magnitude: τ = RF sin RF direction: Right-hand Rule Angular Momentum L : L R × p (vector product) = I ω Moment of Inertia I : I Σ m i R i 2 = R 2 dm Parallel Axes Theorem: axis // to CM axis at distance d : I d = I CM + md 2 Perpendicular Axes Theorem: z -axis planar object: I z = I x + I y Torque and its consequences: Στ i = I α = d L / dt Conservation of Angular Momentum if ( Στ i ) ext = 0 L i = L f Kinetic energy of rotation K rot : K rot = ½ I 2 Equilibrium: Σ F i = 0; Στ i = 0

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Midterm 2 2 Nov 5, 2002 1. MULTIPLE CHOICE QUESTION – Fill the circles in front of all statements below that are . MULTIPLE CHOICE QUESTION – Fill the circles in front of all statements below that are correct. A crate of mass
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PHY131_F02_Midterm2A_solutions - Midterm 2 1 Nov 5 2002...

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