Motion II Momentum and Energy

Momentum Obviously there is a big difference between a truck moving 100 mi/hr and a baseball moving 100 mi/hr. Obviously there is a big difference between a truck moving 100 mi/hr and a baseball moving 100 mi/hr. We want a way to quantify this. We want a way to quantify this. Newton called it Quantity of Motion. We call it Momentum. Newton called it Quantity of Motion. We call it Momentum.

Definition: Momentum = (mass)x(velocity) p=mv Note: momentum is a vector. massive objects can have a large momentum even if they are not moving fast.

Modify Newton’s 2 nd Law Notes: Sometimes we write  t instead of just t. They both represent the time for whatever change occurs in the numerator. Notes: Sometimes we write  t instead of just t. They both represent the time for whatever change occurs in the numerator.

Since p=mv, we have  p=  (mv) Since p=mv, we have  p=  (mv) If m is constant, (often true)  p=m  v If m is constant, (often true)  p=m  v

Yet another definition: Impulse Impulse is just the total change in momentum. We can have a large impulse by applying a weak force for a long time OR a large force for a short time

Examples Baseball Baseball  p=p f - p i  p=p f - p i =mv f – (-mv i ) =m(v f +v i ) F=  p/  t Where  t is the time the bat is in contact with the ball

Realistic numbers Realistic numbers M=0.15kg M=0.15kg Vi = -40m/s Vi = -40m/s Vf = 50m/s Vf = 50m/s  t = (1/2000)s  t = (1/2000)s F=27000N F=27000N a=F/m=180000m/s/s a=F/m=180000m/s/s a=18367g a=18367g slow motion photography slow motion photography slow motion photography slow motion photography

Ion Propulsion Engine: very weak force (about the weight of a paper clip) but for very long times (months) Ion Propulsion Engine: very weak force (about the weight of a paper clip) but for very long times (months)

Crumple Zones on cars allow for a long time for the car to stop. This greatly reduces the average force during accident. Crumple Zones on cars allow for a long time for the car to stop. This greatly reduces the average force during accident.

Landing after jumping Landing after jumping

Conservation of Momentum Newton’s 3 rd Law requires F 1 = -F 2 Newton’s 3 rd Law requires F 1 = -F 2  p 1 /  t=-  p 2 /  t  p 1 /  t=-  p 2 /  t Or Or  p 1 /  t +  p 2 /  t = 0  p 1 /  t +  p 2 /  t = 0 Or Or  p 1 +  p 2 = 0  p 1 +  p 2 = 0 NO NET CHANGE IN MOMENTUM NO NET CHANGE IN MOMENTUM

Example: Cannon 1000kg cannon 1000kg cannon 5kg cannon ball 5kg cannon ball Before it fires P c + P b = 0 P c + P b = 0 Must also be true after it fires. Assume V b =400 m/s M c V c + M b V b =0 M c V c + M b V b =0 V c =-M b V b /M c V c =-M b V b /M c = -(5kg)(400m/s)/(1000kg) = -(5kg)(400m/s)/(1000kg) =-2m/s =-2m/s

Conservation of Momentum Head on collision Head on collision Head on collision Head on collision Football Football Football Train crash Train crash Train crash Train crash Wagon rocket Wagon rocket Wagon rocket Wagon rocket Cannon Fail Cannon Fail Cannon Fail Cannon Fail

ENERGY & WORK In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). In the cannon example, both the cannon and the cannon ball have the same momentum (equal but opposite). Question: Why does a cannon ball do so much more damage than the cannon? Question: Why does a cannon ball do so much more damage than the cannon? Answer: ENERGY Answer: ENERGY

WORK We will begin by considering the “Physics” definition of work. We will begin by considering the “Physics” definition of work. Work = (Force) x (distance traveled in direction of force) Work = (Force) x (distance traveled in direction of force) W=F  d W=F  d Note: 1) if object does not move, NO WORK is done. Note: 1) if object does not move, NO WORK is done. 2) if direction of motion is perpendicular to force, NO WORK is done 2) if direction of motion is perpendicular to force, NO WORK is done

Example Push a block for 5 m using a 10 N force. Push a block for 5 m using a 10 N force. Work = (10N) x (5m) Work = (10N) x (5m) = 50 Nm = 50 Nm = 50 kgm 2 /s 2 = 50 kgm 2 /s 2 = 50 J (Joules) = 50 J (Joules)

I have not done any work if I push against a wall all day long but is does not move. 1. True 2. False

ENERGY is the capacity to do work. ENERGY is the capacity to do work. The release of energy does work, and doing work on something increases its energy The release of energy does work, and doing work on something increases its energy E=W=F  d Two basics type of energy: Kinetic and Potential. Two basics type of energy: Kinetic and Potential.

Kinetic Energy: Energy of Motion Heuristic Derivation: Throw a ball of mass m with a constant force. Heuristic Derivation: Throw a ball of mass m with a constant force. KE = W = F  d= (ma)d But d = ½ at 2 KE = (ma)(½ at 2 ) = ½ m(at) 2 But v = at KE = ½ mv 2

Potential Energy Lift an object through a height, h. Lift an object through a height, h. PE = W = F  d= (mg)h PE = mgh Note: We need to decide where to set h=0.

Other types of energy Electrical Electrical Chemical Chemical Thermal Thermal Nuclear Nuclear

Conservation of Energy We may convert energy from one type to another, but we can never destroy it. We may convert energy from one type to another, but we can never destroy it. We will look at some examples using only PE and KE. We will look at some examples using only PE and KE.KE+PE=const.OR KE i + PE i = KE f + PE f

Drop a rock of 100m cliff Call bottom of cliff h=0 Call bottom of cliff h=0 Initial KE = 0; Initial PE = mgh Initial KE = 0; Initial PE = mgh Final PE = 0 Final PE = 0 Use conservation of energy to find final velocity Use conservation of energy to find final velocity mgh = ½mv 2 v 2 = 2gh

For our 100 m high cliff For our 100 m high cliff Note that this is the same as we got from using kinematics with constant acceleration Note that this is the same as we got from using kinematics with constant acceleration

A 5 kg ball is dropped from the top of the Sears tower in downtown Chicago. Assume that the building is 300 m high and that the ball starts from rest at the top m/s m/s m/s m/s

Pendulum At bottom, all energy is kinetic. At bottom, all energy is kinetic. At top, all energy is potential. At top, all energy is potential. In between, there is a mix of both potential and kinetic energy. In between, there is a mix of both potential and kinetic energy.

Energy Content of a Big Mac 540 Cal 540 Cal But 1Cal=4186 Joules But 1Cal=4186 Joules

How high can we lift a 1kg object with the energy content of 1 Big Mac? PE=mgh PE=mgh h=PE/(mg) h=PE/(mg) PE=2,260,440 J PE=2,260,440 J m=1 kg m=1 kg g=9.8 m/s g=9.8 m/s

2 Big Macs have enough energy content to lift a 1 kg object up to the orbital height of the International Space Station. 2 Big Macs have enough energy content to lift a 1 kg object up to the orbital height of the International Space Station. 150 Big Macs could lift a person to the same height. 150 Big Macs could lift a person to the same height. It would take about 4,000,000 Big Macs to get the space shuttle to the ISS height. It would take about 4,000,000 Big Macs to get the space shuttle to the ISS height. Note: McDonald’s sells approximately 550,000,000 Big Macs per year. Note: McDonald’s sells approximately 550,000,000 Big Macs per year.

Revisit: Cannon Momentum 1000kg cannon 1000kg cannon 5kg cannon ball 5kg cannon ball Before it fires P c + P b = 0 P c + P b = 0 Must also be true after it fires. Assume V b =400 m/s M c V c + M b V b =0 M c V c + M b V b =0 V c =-M b V b /M c V c =-M b V b /M c = -(5kg)(400m/s)/(1000kg) = -(5kg)(400m/s)/(1000kg) =-2m/s =-2m/s

Cannon:Energy KE b = ½ mv 2 = 0.5 (5kg)(400m/s) 2 = 400,000 kgm 2 /s 2 = 400,000 kgm 2 /s 2 =400,000 J KE c = ½ mv 2 = 0.5 (1000kg)(2m/s) 2 = 2,000 kgm 2 /s 2 = 2,000 kgm 2 /s 2 =2,000 J Note: Cannon Ball has 200 times more ENERGY

Important Equations