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Momentum and Energy Momentum is Mass x Velocity: Each Plane has Velocity v Each Plane has Mass m Each Plane has Momentum p = mv Momentum Has Direction Though they have the same masses and speeds, their momenta are different. The Direction of the Momentum is Vital By convention, if the momentum points to the right or up, it is positive. Similarly, if the momentum points to the left or down, it is negative. Impulse Means a Change in Momentum Consider a bouncing ball: pafter = momentum right after bouncing Impulse = pafter - pbefore = F Dt Note that pbefore < 0 and pafter > 0 F > 0. pbefore = momentum just before bouncing The ball is in contact with the floor for a period of time Dt. The force exerted by the floor causing the ball to bounce is F. The Impulse-Momentum Theorem and Newton’s 3rd Law on a Bouncing Object: Force of wall Dp Fon ball = on ball: Dt Fon ball = -Fon wall; both forces are applied for the same period of time, Dt. Therefore, the changes in momenta are equal but opposite. When Two (or More) Objects Collide, the Total Momentum, P, is Conserved v1,before m1 v1,after v2,before m2 Pbefore = m1v1,before + m2v2,before v2,after m1 m2 Pafter = m1v1,after + m2v2,after = m1v1,before + Dp1 + m2v2,before + Dp2 = m1v1,before + Dp1 + m2v2,before - Dp1 = m1v1,before + m2v2,before = Pbefore If You Exert a Force Over Any Distance, You Have Done Work F F d Work = Force × Distance W= F × d Work is a form of energy! There are Different Types of Energy Mechanical -Energy of Motion Thermal -Energy of Heat Nuclear -- Energy in the Atom Electromagnetic -Energy of Electricity Energy is Measured in “Joules” 1 Joule = 1 Newton x 1 meter = 1 kilogram·meter2/second2 James Prescott Joule, 1818 - 1889 (He showed heat and energy are the same thing) Energy is Always Being Transformed From One Kind to Another A falling object transforms gravitational potential energy into kinetic energy An explosion may transform chemical energy into thermal energy The Total Energy in a Reaction Remains Constant! 5323 Joules of Energy in Chemical or Physical Reaction 5323 Joules of Energy out (possibly in different forms) The Work-Energy Theorem: Although it sounds intimidating, the WorkEnergy Theorem is not a difficult concept. In short, if you do work on an object, you change that object’s total energy by exactly the same amount of work you put into it. Here, you are pushing the block Fyou Fyou The block keeps moving vobject d Wdone by you = Fyoud Object’s Change in KE = Fyoud Kinetic Energy is the Energy Associated with Motion Kinetic Energy increases with the mass m that is in motion Kinetic Energy increases with the speed v of the mass Kinetic Energy = ½mv2 If I do work W to increase an object’s kinetic energy, then KEfinal = KEinitial + W Another Type of Mechanical Energy is “Potential” Energy If this mass m is held suspended at a height h then it has gravitational potential energy. It is equal to the force due to gravity, mg, times the height above the ground: m h GPE = mgh “Potential Energy” is Like Having Stored Energy m GPE = mgh If the object starts from rest, its initial kinetic energy is zero. m As the object falls, gravitational potential energy is converted into kinetic energy, KE = ½mv2. Question: Two people do the same work, but one does it more quickly than the other. If the work done by each is the same, what quantity is different? The Answer is “POWER” Work Performed Power = Time Spent Doing the Work By this definition, the less time you spend to perform a certain amount of work, the more power you exert during that period of time. Power Has Units of Watts 1 Watt = 1 Joule/second 1 kilowatt·hour = 1000 watts · 1 hour = 1000 Joules/sec · 3600 sec = 3,600,000 Joules James Watt, 1736 - 1819 Inventor of the Steam Engine (The kW ·hr is a measure of energy, NOT of power)