Physics_notes_4_with_solutions

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: ݌ Ԧൌ݉ݒ 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 ൌ∆݌ Ԧൌ݌ 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 ݐൌ0 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. Sound familiar? Since energy and momentum are both conserved, they can be used in combination to
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Physics_notes_4_with_solutions - Energy Diagrams Momentum...

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