Final Exam. conflicts with the regular time. Two students have confirmed conflicts with me and will take the

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1 Reiew 3

2 Final Exam A common final exam time is scheduled d for all sections of Phsics 31 Time: Wednesda December 14, from 8-10 pm. Location for section 00 : BPS 1410 (our regular lecture room). This information can also be found on our course schedule page An alternate exam time will be scheduled for students who hae conflicts with the regular time. Two students hae confirmed conflicts with me and will take the exam then. You must contact me b and obtain permission from me to take the exam at the alternate time. If ou fail to do this, ou will be barred from taking the alternate final exam. RCPD students should arrange to take their final exam at Besse. Alternate time: Tuesda December 13, from 1-3 pm Location: BPS 1410 (this room)

3 Concepts/equations: o s: + t is the elocit in the "stationar " frame is the elocit in the "moing" " frame t is the elocit of the "moing" Exam 1 problem 4 frame Examples of alternate formulations Gie boat and rier speed, time and ask for distances across and downstream. Gie boat and water speed, width and ask for distance downstream. Gie boat and water speed, width and ask for total distance. Gie boat speed, rier speed and distance downstream and ask for total distance. Gie boat speed, rier speed and distance downstream and ask for distance across.

4 Exam 1 problem 5 Concepts/equations: o s: ΔPE 1 KE m PE PE mg f ( ) 0 f 0 Conseration of energ E KE f + PE f KE 0 + PE 0 Examples of alternate formulations AskforatB B. Gie at C and ask for height at A. Gie at B or C and ask for 0.

5 Concepts/equations: o s: Work: W FΔs cos θ Kinetic energ: KE 1 m ( ) F x xδ Work-energ theorem: W total KE KE 0 f Examples of alternate formulations Gie elocit ask for F. Gie a different shape for the cure. Exam 1 problem 6

6 Concepts/equations: o s: Net force on each object in the problem anishes. N i i W F 0 mg Exam 1 problem 7 Examples of alternate formulations Gie Tension, mass and ask for angle. Gie T and angle and ask for mass. The tension in the two wires supporting the mass of 9 kg is 118 N, what is the angle? i F 0 Tsinθ mg i, mg sinθ T o θ sin ( )

7 Concepts/equation o Newton s second law: F ma tension forces Newton s 3 d Law: F of on1 F of1on Examples of alternate formulations Gie Tension, F, M 1, M and ask for angle. Gie T, F, M, and angle and ask for M 1. Ke is that the phsical situation is the same, but the question is different. Exam 1 problem 8

8 Concepts/equation Newton s second law: F net ma tension forces W mg Grait: Normal force: Friction forces: fs < μsn Exam 1 problem 9. Examples of alternate formulations Consider the figure aboe with M kg and μ Gie M, µ s and ask for M 1. s.17, what is the minimum mass for M that would oercome the static friction Gie M 1 and M and ask for µ s. force on M 1? Put table and masses on the Moon or some other planet where g is different, Gie M, µ s and ask for M 1. Ke is that the phsical situation is the same, but the question is different.

9 Concepts/equation ( θ) τ Fr sin 0 I i m r i i Exam problem 1 τ Iα 0 L I ω is consered ΔL0 1 KE rot I ω Examples of alternate formulations Make into a conceptual problem. Gie the initial elocit and ask the final elocit. Ask the ratio of initial/final elocit. Ask for the initial elocit and puck mass Ke is that the phsical situation is the same, but the question is different.

10 Concepts/equation Conseration of momentum p + p p + p 1,i,i 1,f,f Exam problem Examples of alternate formulations Gie final elocities and ask initial elocit of the bo. Make man to be at rest initiall. Gie all elocities of man and bo and the mass of the man. Ask the mass of the bo. Make the man to be moing initiall as well. Gie both final elocities and the initial elocit of the bo and ask the initial elocit of the man. Make the collision in two dimensions. Ke is that the phsical situation is the same, but the question is different.

11 Concepts/equation Newton s second law for rotational motion, τ I α Rotational kinematics: Δ θ ωt ω ω0 + αt Exam problem 3 A to Ferris wheel with moment of inertia of 476 Nm is at rest and then experiences a torque of 18 Nm that lasts for 1 s. What is the final angular elocit? 1 1 ω ( ω + ω0 ) Δθ ( ω + ω0 ) t 1 Δθ ω0t + αt ω ω0 + αδθ τ 18 α 0.038rad / s I 476 Examples of alternate formulations ω αt 0.038rad / s 1s 0.45rad / s Gie moment of inertia, torque, time required, ask the final angular speed. Gie moment of inertia, sole for torque. Gie moment of inertia, torque, sole for time required to get to final speed. Ke is that the phsical situation is the same, but the question is different.

12 Concepts/equation Pendulum, simple harmonic motion: 1 g f ω ; π π L L T 1/f π g θ θ cos( π ft); max Examples of alternate formulations Exam problem 4 Ask for the length of the pendulum. Sa that there are two pendula on the two different planets. Gie periods or frequencies and ask for the ratio of the lengths. Change grait AND length b same ratio. Change length onl. Ke is that the phsical situation is the same, but the question is different.

13 Concepts/equation o Stress strain relationship: Exam problem 5 ΔF F ΔL L Y A L 0 Examples of alternate formulations For this one, ou can interchangeabl sole for either F, m, A, delta L, L, or diameter. Ke is that the phsical situation is the same, but the question is different. A mass of 40 kg is suspended from a steel wire of length.10 m. The wire stretches b 0. mm. What is the diameter of the wire? Young s modulus for steel is 00x10 9 N/m.

14 Concepts/equation Newton s law of uniersal graitation: GMplanet msarah F W R Exam problem 6 Sarah planet Sarah weighs 408 N on planet X, which has 4 times the mass of Earth and twice its diameter. What does she weigh on earth? Examples of alternate formulations You are gien W X,R X /R E,M X /M E and asked for W E. You are gien W E, W X and M X /M E and asked for R X /R E. You are gien W E, W X and R X /R E and asked for M X /M E. You are gien W X, W E, R X /R E, M E and asked dfor M X. Ke is that the phsical situation is the same, but the question is different.

15 Concepts/equation centripetal acceleration a c t r r ω Exam problem 7 ω t ; r θ ω t Examples of alternate formulations We gie r, a c and ask for t. We gie a c, t and ask for r. Ke is that the phsical situation is the same, but the question is different. A supersonic plane follows a circular path of radius 75 km. It experiences an acceleration of 7.5 m/s. What is the speed of the plane?

16 gt downwards 9.8 m/s g ( )t gt o Δ g gt t Δ Δ t x x x x 0 0 Δ PHY

17 Concepts/equations: ΔPE KE PE f 1 m PE mg ( ) 0 f 0 Conseration of energ E KE f + PE f KE 0 + PE 0 Work energ theorem KEf KE0 Wfriction

18 Static equilibrium τ i 0 and F i 0 i i calculation of torque τ Fr sin ( θ) PHY

19 Conseration p + p p of momentum + p 1,i,i 1,f,f PHY

20 PHY