Physics_notes_4_with_solutions - Energy Diagrams Momentum...

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Energy Diagrams, Momentum, Impulse, Conservation of Momentum, Rocket Propulsion, Center of Mass Energy Diagrams A plot of the potential energy of a system. Total energy (constant if there are no non conservative forces) is also plotted as a horizontal line. Note the stable and unstable equilibrium points. Be able to plot the forces acting on an object based on its potential energy curve [pg 235 6]. Impulse and Linear Momentum Momentum is a vector quantity defined by: ݌ Ԧ ൌ ݉ݒ Ԧ It is a vector quantity, so it has ݔ, ݕ, and ݖ components. Momentum is very useful for describing collisions (billiard balls, explosions, car crashes, recoil, rocket burning fuel, and the like…). Momentum is important enough that we define a new term for the change in momentum – impulse – given by ܬ ሬԦ ൌ ∆݌ Ԧ ൌ ݌ Ԧ െ ݌ Ԧ . More generally, impulse can be described as the net force acting on an object during a time interval. ܬ Ԧ ൌ ׬ ܨ Ԧ ݀ݐ . Impulse relates the net force applied to an object to its change in momentum. Note that impulse is also a vector. Example (Impulse) – 8.9 A hockey puck with mass ݉ is moving on an icy, frictionless, horizontal surface. At ݐ ൌ 0 , the puck is moving to the right with speed ݒ . a) Calculate the velocity of the puck (magnitude and direction) after a force of ܨ Ԧ directed to the right has been applied for ݐ seconds. b) If, instead, a force of ܨ Ԧ directed to the left is applied from ݐ ൌ 0 to ݐ ൌ ݐ , what is the final velocity of the puck? U(x) U(x) E U(x) E U(x) E
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Energy Diagrams, Momentum, Impulse, Conservation of Momentum, Rocket Propulsion, Center of Mass Example (Impulse) – 8.12 A bat strikes a baseball with mass ݉ . Just before impact, the ball is traveling horizontally to the right with speed ݒ , and it leaves the bat traveling to the left at an angle of ߠ above horizontal with a speed ݒ . If the ball and bat are in contact for ݐ seconds, find the horizontal and vertical components of the average force on the ball. Solution: ܨ ሺെݒ cos ߠ െ ݒ ሻ ܨ ሺݒ sin ߠሻ Conservation of Momentum Momentum is also conserved, as long as there are no external forces applied to the system.
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