Momentum and Energy

Momentum is Mass x Velocity: Each Plane has Mass m Each Plane has Velocity v 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: p before = momentum just before bouncing p after = momentum right after bouncing Impulse = p after - p before = F  t The ball is in contact with the floor for a period of time  t. The force exerted by the floor causing the ball to bounce is F. Note that p before 0  F > 0.

The Impulse-Momentum Theorem and Newton’s 3 rd Law on a Bouncing Object: F on ball = pp tt Force of wall on ball: F on ball = -F on wall ; both forces are applied for the same period of time,  t. Therefore, the changes in momenta are equal but opposite.

When Two (or More) Objects Collide, the Total Momentum, P, is Conserved m1m1 v 1,before m2m2 v 2,before P before = m 1 v 1,before + m 2 v 2,before m1m1 m2m2 v 1,after v 2,after P after = m 1 v 1,after + m 2 v 2,after = m 1 v 1,before +  p 1 + m 2 v 2,before +  p 2 = m 1 v 1,before +  p 1 + m 2 v 2,before -  p 1 = m 1 v 1,before + m 2 v 2,before = P before

If You Exert a Force Over Any Distance, You Have Done Work FF d Work = Force × Distance W = F × d Work is a form of energy!

There are Different Types of Energy Mechanical -- Energy of Motion Nuclear -- Energy in the Atom Thermal -- Energy of Heat Electromagnetic -- Energy of Electricity

Energy is Measured in “Joules” James Prescott Joule, (He showed heat and energy are the same thing) 1 Joule = 1 Newton x 1 meter = 1 kilogram·meter 2 /second 2

Energy is Always Being Transformed From One Kind to Another A falling object trans- forms gravitational potential energy into kinetic energy An explosion may trans- form chemical energy into thermal energy

The Total Energy in a Reaction Remains Constant! 5323 Joules of Energy in 5323 Joules of Energy out Chemical or Physical Reaction (possibly in different forms)

The Work-Energy Theorem: Although it sounds intimidating, the Work- Energy 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. F you d W done by you = F you dObject’s Change in KE = F you d v object F you Here, you are pushing the blockThe block keeps moving

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 = ½mv 2 If I do work W to increase an object’s kinetic energy, then KE final = KE initial + W

Another Type of Mechanical Energy is “Potential” Energy m h 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: GPE = mgh

“Potential Energy” is Like Having Stored Energy m GPE = mgh m As the object falls, gravitational potential energy is converted into kinetic energy, KE = ½mv 2. If the object starts from rest, its initial kinetic energy is zero.

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” Power = Work Performed 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 James Watt, Inventor of the Steam Engine 1 Watt = 1 Joule/second 1 kilowatt·hour = 1000 watts · 1 hour = 1000 Joules/sec · 3600 sec = 3,600,000 Joules (The kW ·hr is a measure of energy, NOT of power)