Lecture8 - PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 8 •...

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Unformatted text preview: PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 8 • Work for nonconstant force • Spring force • Potential Energy of Spring • Power Last Lecture F = -κξ PE = 1 2 κξ 2 P = D W D t = D KE D t P = Fv F x Chapter 6 Momentum and Collisions Momentum Definition: Newton’s 2 nd Law: r p = μ ρ ω ρ F = m D r v D t ρ F = D r p D t Conservation of Momentum True for isolated particles (no external forces) Proof: Recall F 12 =-F 21 , (Newton’s 3 rd Law) for isolated particles never changes! ρ F 12 + r F 21 = 0 D r p 1 D t + D r p 2 D t = 0 r ∆ ρ p 1 + D r p 2 = 0 r p 1 f + r p 2 f = r p 1 i + r p 2 i ρ p i Momentum is a Vector quantity • Both Σ p x and Σ p y are conserved p x = μ ω ξ π ψ = μ ω ψ Example 6.1 An astronaut of mass 80 kg pushes away from a space station by throwing a 0.75-kg wrench which moves with a velocity of 24 m/s relative to the original frame of the astronaut. What is the astronaut’s recoil speed? 0.225 m/s Center of mass does not accelerate X cm μ 1 ξ 1 + μ 2 ξ 2 + μ 3 ξ 3 + ... (μ 1 + μ 2 + μ 3 + ...29 ∆ X cm = m 1 D x 1 + m 2 D x 2 + m 3 D x 3 + ... ( m 1 + m 2 + m 3 + ...) = D t m 1 (D x 1 / D t ) + m 2 (D x 2 / D t ) + m 3 (D x 3 / D t ) + ... ( m 1 + m 2 + m 3 + ...) = D t p 1 + p 2 + p 3 + ... ( m 1 + m 2 + m 3 + ...) = 0 if total P iszero Example 6.2 Ted and his ice-boat (combined mass = 240 kg) rest on the frictionless surface of a frozen lake. A heavy rope (mass of 80 kg and length of 100 m) is laid out in a line along the top of the lake. Initially, Ted and the rope are at rest. At time t=0, Ted turns on a wench which winds 0.5 m of rope onto the boat every second....
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This note was uploaded on 07/25/2008 for the course PHY 231 taught by Professor Smith during the Spring '08 term at Michigan State University.

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Lecture8 - PHYSICS 231 INTRODUCTORY PHYSICS I Lecture 8 •...

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