PHY183-Lecture34

# PHY183-Lecture34 - Final Exam Our Common Comprehensive...

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1 March 28, 2012 Physics for Scientists&Engineers 1 1 Final Exam Our Common Comprehensive Final Exam is on Thursday, May 3 rd from 8:00-10:00PM Location Chemistry (CEM) room 138 Two 8.5 inch by 11 inch sheets of notes (both sides) Calculator Alternate Final Exam University approved excuses only Email me with your reason for taking the exam at the alternate time prior to Friday, April 6 Wednesday, May 2, 7:45 – 9:45 AM (room TBA) March 28, 2012 Physics for Scientists&Engineers 1 2 Physics for Scientists & Engineers 1 Spring Semester 2012 Lecture 34 Gravitational Potential Energy and Gravitational Potential Kepler’s First Laws March 28, 2012 Physics for Scientists&Engineers 1 3 Clicker Quiz Consider the force of gravity between two objects. You increase the distance between the objects by a factor of three, the gravitational force between the two objects will A) increase by a factor of 3 B) decrease by a factor of 3 C) increase by a factor of 9 D) decrease by a factor of 9 E) stay the same March 28, 2012 Physics for Scientists&Engineers 1 4 Clicker Quiz Solution Consider the force of gravity between two objects. When you increase the distance between the objects by a factor of three, the gravitational force between the two objects will A) increase by a factor of 3 B) decrease by a factor of 3 C) increase by a factor of 9 D) decrease by a factor of 9 E) stay the same F ( r ) = G m 1 m 2 r 2 F 2 F 1 = G m 1 m 2 r 2 2 G m 1 m 2 r 1 2 = r 1 2 r 2 2 = r 1 2 3 r 1 () 2 = 1 9 decrease by a factor of 9 March 28, 2012 Physics for Scientists&Engineers 1 5 Potential Energy Previously we defined the gravitational potential energy assuming a constant gravitational force Now, new force law: Normalize so that the potential energy becomes 0 at infinite separation: F = − mg U = mgh Ur () − U () = Fr ' dr ' r = Gm 1 m 2 r ' 2 dr ' r U Gm 1 m 2 1 r ' 2 dr ' r =− Gm 1 m 2 1 r ' r G m 1 m 2 r Note: always U < 0 ()=− G m 1 m 2 r March 28, 2012 Physics for Scientists&Engineers 1 6 Gravitational Potential Energy Superposition of gravitational potential energy from pairs Example: potential energy from three objects How do we get our old result ( mgh ) back? For h R E Potential energy difference U = U 12 + U 13 + U 32 G m 1 m 2 r 1 r 2 G m 1 m 3 r 1 r 3 G m 3 m 2 r 3 r 2 U ( h ) G M E m R E + h ≈− GM E m R E + GM E m R E 2 h gmR E + mgh Δ U = U ( h ) U (0) = U ( h ) = ( gmR E + mgh ) ( gmR E ) = mgh additive constant

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2 March 28, 2012 Physics for Scientists&Engineers 1 7 Escape Speed Total energy of two objects in gravitational interaction with each other: Special case: one of the objects is Earth; work in frame where Earth is not moving total energy What is the speed with which this object has to start from the surface of Earth and escape to infinity?
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## This note was uploaded on 04/02/2012 for the course PHY 183 taught by Professor Wolf during the Spring '08 term at Michigan State University.

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PHY183-Lecture34 - Final Exam Our Common Comprehensive...

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