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Physics 321 Hour 3 Application of Newton’s Laws/Drag Forces Consequences of Relativity • Momentum becomes π = π π£ = π0 πΎ π£ • Kinetic energy becomes π = ππ 2 − π0 π 2 • Potential energy becomes hazy • Momentum is conserved “asymptotically” Problem 1 A mass hangs from a string from the roof of a train car accelerating with π. What is θ? θ π Problem 2 A sphere of mass m, radius R, and moment of inertia I rolls on a horizontal surface without slipping when a tension T is applied. What is the acceleration? π Problem 3 A large mass M and a small mass m are π stacked on each other. A tension T is applied to the large mass. The coefficient of static friction is μs and the coefficient of sliding friction is μ. How big can T become without the top mass slipping? Drag Forces 1) Forces of the form πΉ = −|π … |π£ cause an object to slow down. Why? Drag Forces 2) A typical drag force can have linear and quadratic components: How can we write this in one dimension (eg, for free fall)? πΉπ = −π1 π¦ + π2 π¦ 2 How can we write this in three dimensions? πΉπ = −π1 π£ − π2 π£ π£ Free fall with linear drag 3) The differential equation: ππ£ = −ππ − π1 π£ ππ 4) Terminal velocity – when π£ = 0, π£ = − π1 Mathematica 1. Drag3-1.nb 2. LinvsQuad.nb