Energy and Momentum

Energy and MomentumTypes of EnergyEnergy is the capacity for an object to do workFor example, when a car moves, the engine performs work to get the car going.There are many different types of energy, including: electrical, kinetic, gravitational potential, and elastic potential to name a few.A more complete list can be found on p. 124Energy TransformationAn energy transformation occurs whenever energy changes from one form into another.Examples of this would be a ball being held above the ground (gravitational potential) and then being released to fall to the ground (kinetic).Look at #2 on p 125 to get the class thinking about possible transformations3WorkWorkThis is the energy transferred to an objectThe object must move a distance as a result of the force appliedDoes it matter what direction the object moves??Do the waiter example about work5How to calculate workWork requires a forceWork requires a distanceThis leads us to say: WF and WdThis gives us: W = F dThe units are Newton Meters (Nm) or, more commonly, Joules (J)ExamplesA 600 N force is applied by a person to a dresser that moves 2 m. Find the work done if the force and the displacement areParallelAt right anglesOppositely directedA horse pulls a barge along a canal with a rope in which the tension is 1000N. The rope is at an angle of 10 with the towpath and the direction of the bargeHow much work is done by the horse in pulling the barge 100m?What is the net force on the barge?Remember!!!!For there to be work, Hw: p.128 #s 1-6 and 89Positive and Negative WorkAny force applied in the same plane causes work to be doneIf the force makes the object increase in speed, then it is positive workIf the force makes the object slow its speed, then it is negative work. These forces are called Dissipative ForcesAll friction is negative work.GravityWhen we lift something up, we do work, why is this?When we look at this type of work, we still must look at the force we are working withFg = mgThis lead to the followingW = FgdW = mgd

ExampleA bag of groceries of mass 8.1 kg is raised vertically without acceleration from the floor to a counter top, over a distance of 92 cm. DetermineThe force needed to raise the bag without acceleration.The work done on the bag against the force of gravitySee p. 129 Have them read the section on zero work, p. 130 and do questions 9-15 Hw: p. 131 #s 1-712Mechanical EnergyMechanical energyThere are 2 types of mechanical energyGravitational Potential EnergyKinetic EnergyGravitational Potential EnergyThis is energy that can be used to do work at a lower levelKinetic EnergyThis is the energy of motionDetermining Potential energyexampleAssume that a 59 kg pole vaulter must raise their center of mass from 1.1 m off the ground to 4.6 m off the ground. What is the jumpers gravitational potential energy at the top of the bar relative to where the jumper started to jump?Ep = mghEp = (59)(9.81)(4.6-1.1)Ep = 2.0 x 103 J

Applications of mechanical energyGrain AugerPile DriversHydro DamsWe use this in Red Lake everydayDetermining kinetic energyIf you are interested in how the formula is generated, see p. 134Kinetic energy is the energy of motion, so what do we need?Ek = mv2exampleDetermine the amount of kinetic energy of a 48 g dart travelling at a speed of 3.4 m/s.Ek = mv2Ek = (.048)(3.4)2Ek = 0.28 JHw: p.135 #s 8 - 1319Law of conservation of energyEnergy conservationWe know that there are many types of energy transformationsWhen energy changes forms, energy is conservedWhat does this mean?Energy is never lost, it just changes formExampleSimple Harmonic MotionPeriodic MotionMotion that repeats itself over and overEx: heart beats, ticking clock, moving on a swingThe time it takes for one complete cycle of the motion is called the .

PeriodOther Terms to KnowCycle One complete back and forth motionFrequency the number of cycles per unit time. It is measured in Hertz (Hz)Displacement the distance an object moves from the equilibrium positionAmplitude the maximum displacementSimple Harmonic Motion (SHM)A type of periodic motionObjects that vibrate with SHM are called Simple Harmonic OscillatorsAn example of this is a mass on a spring, pendulums, and waves

Mass on a springWhen there is a mass on a spring, there are 2 forces that are acting on it.Gravity and the Tension of the springTension on the spring is governed by Hookes Law

Hookes LawF is Forcek is the spring constantX is the displacementWhen the spring is stretched FT > Fg then the mass moves upwardsWhen the spring is compressed Fg > FT then the mass moves downwards Hookes Law Example

A mass of 15.0 kg is suspended from a spring. If the spring has a spring constant is 6.00 N/m, what is the restoring force of the spring when the mass is 0.30 m from equilibrium?F = -kxF = -(6.00 N/m)(0.30 m)F = -1.8 N

MASS ON A SPRINGMeStretch & ReleaseA

k = the spring constant in N/m29Mass on a Spring ExampleHookes Law Cont.If there was no force to slow the motion down, it would continue foreverThe force that causes the slowing of the motion is called the Restoring ForceThe Restoring force is governed by the spring constant, k

timeDAMPINGDISPLACEMENTINITIAL AMPLITUDETHE AMPLITUDE DECAYS EXPONENTIALLY WITH TIMEHookes Law Cont.When there is a Restoring force, the systems will become dampedWhere is this idea of a damped system used in your daily life???THE PENDULUMThe period, T, is the time for one complete cycle.

lPendulum ExampleEnergy in SHMEnergy in SHM Cont.

Circular motion and SHMAppletImpulse and MomentumImpulse and MomentumImpulse and momentum play important roles in sports.Bowling

Baseball

Tennis

Soccer

Karate

Foot ball

Golf

Impulse, pThe impulse J of a force is the product of the average force and the time interval Dt during which the force acts:Impulse is a vector quantity and has the same direction as the average force.SI Unit of Impulse: newton second = (N s)Momentum, pThe linear momentum p of an object is the product of the objects mass m and velocity v:Linear momentum is a vector quantity that points in the same direction as the velocity.SI Unit of Linear Momentum: kilogram meter/second = (kg m/s)So Whats Momentum ?Momentum = mass x velocity Momentum is a measure of inertia in motionThis can be abbreviated to :momentum = mv

Or, if direction is not an important factor : momentum = mass x speed

So, A really slow moving truck and an extremely fast roller skate can have the same momentum.Question :Under what circumstances would the roller skate and the truck have the same momentum ?The roller skate and truck can have the same momentum if the ratio of the speed of the skate to the speed of the truck is the same as the ratio of the mass of the truck to the mass of the skate.A 1000 kg truck moving at 0.01 m/sec has the same momentum as a 1 kg skate moving at 10 m/sec. Both have a momentum of 10 kg m/sec. ( 1000 x .01 = 1 x 10 = 10 ) 1000 kg1 kg.01 m/sec10 m/secImpulse and MomentumIf momentum changes, its because mass or velocity change.Most often mass doesnt change so velocity changes and that is acceleration.And mass x acceleration = force Applying a force over a time interval to an object changes the momentumForce x time = Impulse Impulse = F t or Ft = mvFt = mvFORCEMOMENTUMAn object at rest has no momentum, why?Because anything times zero is zero(the velocity component is zero for an object at rest)To INCREASE MOMENTUM, apply the greatest force possible for as long as possible.Examples : pulling a sling shot drawing an arrow in a bow all the way back a long cannon for maximum range hitting a golf ball or a baseball . (follow through is important for these !)TIMEHitting a baseball

Hitting a baseball

Hitting a baseball

Q: How can we determine the impulse?Hitting a baseball

Hitting a baseball

Example

A baseball (m = 0.14 kg) has an initial velocity of v0 = 38 m/s as it approaches a bat. We have chosen the direction of approach as the negative direction. The bat applies an average force that is much larger than the weight of the ball, and the ball departs from the bat with a final velocity of vf = +38 m/s. Determine the impulse applied to the ball by the bat. MOMENTUMSOME VOCABULARY : impulse : impact force X time (newton.sec) Ft = impulse

impact : the force acting on an object (N) usually when it hits something.

impact forces : average force of impact

Decreasing Momentum

Which would it be more safe to hit in a car ?

Knowing the physics helps us understand why hitting a soft object is better than hitting a hard one. MOMENTUMmvmvFtFtMOMENTUMIn each case, the momentum is decreased by the same amount or impulse (force x time)

Hitting the haystack extends the impact time (the time in which the momentum is brought to zero).

The longer impact time reduces the force of impact and decreases the deceleration.

Whenever it is desired to decrease the force of impact, extend the time of impact !

DECREASING MOMENTUMIf the time of impact is increased by 100 times (say from .01 sec to 1 sec), then the force of impact is reduced by 100 times (say to something survivable).

EXAMPLES :Padded dashboards on carsAirbags in cars or safety nets in circusesMoving your hand backward as you catch a fast-moving ball with your bare hand or a boxer moving with a punch.Flexing your knees when jumping from a higher place to the ground or elastic cords for bungee jumpingUsing wrestling mats instead of hardwood floors.Dropping a glass dish onto a carpet instead of a sidewalk.EXAMPLES OF DECREASING MOMENTUMBruiser Bruno on

Increased impact time reduces force of impactBarney Jervais on bungee Jumping POOF !CRUNCH !Ft = change in momentumFt = change in momentumFt = mv applies here.mv = the momentum gained before the cord begins to stretch that we wish to change. Ft = the impulse the cord supplies to reduce the momentum to zero.Because the rubber cord stretches fora long time the average force on the jumper is small. Questions : When a dish falls, will the impulse be less if it lands on a carpet than if it lands on a hard ceramic tile floor ? The impulse would be the same for either surface because there is the same momentum change for each. It is the force that is less for the impulse on the carpet because of the greater time of momentum change. There is a difference between impulse and impact.

If a boxer is able to increase the impact time by 5 times by riding with a punch, by how much will the force of impact be reduced?Since the time of impact increases by 5 times, the force of impact will be reduced by 5 times. Hailstones Versus Raindrops

Unlike rain, hail usually does not come to rest after striking a surface. Instead, the hailstones bounce off the roof of the car. If hail fell instead of rain, would the force on the roof be smaller than, equal to, or greater?Hailstones Versus Raindrops

Unlike rain, hail usually does not come to rest after striking a surface. Instead, the hailstones bounce off the roof of the car. If hail fell instead of rain, would the force on the roof be smaller than, equal to, or greater?Answer: GreaterBOUNCINGIMPULSES ARE GREATER WHEN AN OBJECT BOUNCESThe impulse required to bring an object to a stop and then to throw it back upward again is greater than the impulse required to merely bring the object to a stop. When a martial artist breaks boards,does their hand bounce?Is impulse or momentum greater ?

Example : The Pelton Wheel.

CONSERVATION OF MOMENTUMTo accelerate an object, a force must be applied. The force or impulse on the object must come from outside the object.

EXAMPLES : The air in a basketball, sitting in a car and pushing on the dashboard or sitting in a boat and blowing on the sail dont create movement. Internal forces like these are balanced and cancel each other. If no outside force is present, no change in momentum is possible. Definitions of Terms

Internal forces Forces that the objects within the system exert on each other.External forces Forces exerted on the objects by agents that are external to the system.An isolated system is one for which the vector sum of the external forces acting on the system is zero.The Law of Conservation of MomentumUnless there is an external force acting on a system, the momentum of the system remains unchanged.

This means that, when all of the forces are internal (for EXAMPLE: the nucleus of an atom undergoing radioactive decay, cars colliding, or stars exploding the net momentum of the system before and after the event is the same.

The Law of Conservation of MomentumNo change in momentum occurs unless outside force actsIf objects collide, Total momentum before = total momentum after for both objectsFor any system, this holds trueIMPULSEMOMENTUM THEOREM

When a net force acts on an object, the impulse of the net force is equal to the change in momentum of the object: QUESTIONS1. Newtons second law states that if no net force is exerted on a system, no acceleration occurs. Does it follow that no change in momentum occurs?No acceleration means that no change occurs in velocity and therefore no change in momentum.

2. Newtons 3rd law states that the forces exerted on a cannon and cannonball are equal and opposite. Does it follow that the impulse exerted on the cannon and cannonball are also equal and opposite?Since the time interval and forces are equal and opposite, the impulses (F x t) are also equal and opposite.EXAMPLE5 Assembling a Freight TrainA freight train is being assembled in a switching yard, and Figure 7.10 shows two boxcars. Car 1 has a mass of m1 = 65103 kg and moves at a velocity of v01 = +0.80 m/s. Car 2, with a mass of m2 = 92103 kg and a velocity of v02 = +1.3 m/s, overtakes car 1 and couples to it. Neglecting friction, find the common velocity vf of the cars after they become coupled.

EXAMPLE6 Ice SkatersStarting from rest, two skaters push off against each other on smooth level ice, where friction is negligible. As Figure 7.11a shows, one is a woman (m1 = 54 kg), and one is a man (m2 = 88 kg). Part b of the drawing shows that the woman moves away with a velocity of vf1 = +2.5 m/s. Find the recoil velocity vf2 of the man.

CollisionsCollisions are often classified according to whether the total kinetic energy changes during the collision:1.Elastic collisionOne in which the total kinetic energy of the system after the collision is equal to the total kinetic energy before the collision. 2.Inelastic collisionOne in which the total kinetic energy of the system is not the same before and after the collision; if the objects stick together after colliding, the collision is said to be completely inelastic.

Collisions in One Dimension

Apply the conservation of momentum.If the collision is elastic, apply the conservation of energy. COLLISIONSELASTIC COLLISIONS

INELASTIC COLLISIONSMomentum transfer from one Object to another .

Is a Newtons cradle like the one Pictured here, an example of an elastic or inelastic collision?Problem Solving #1(write this down)A 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is at rest. Find the velocity of the fish immediately after lunch. System is both fish, so .. net momentum before = net momentum after ((mv big fish) + (mvsmall fish))before = (m big fish+ msmall fish)(Vboth)after

(6 kg)(1 m/sec) + (2 kg)(0 m/sec) = (6 kg + 2 kg)(vafter) 6 kg.m/sec = (8 kg)(vafter) vafter = 6 kg.m/sec / 8 kg 8 kg vafter = m/secvafter = Problem Solving #2Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is swimming towards it at 2 m/sec. Find the velocity of the fish immediately after lunch. System is both fish, so. total momentum before = total momentum after (total mv)before = (total mv)after ((mv big fish) + (mvsmall fish))before = (mv big fish) + (mvsmall fish))after

(6 kg)(1 m/s) + (2 kg)(-2 m/s) = (6 kg + 2 kg)(vafter) 6 kg.m/sec + -4 kg.m/sec = (8 kg)(vafter) vafter = 2 kg.m/sec / 8 kg 8 kg vafter = m/sec

vafter = Problem Solving #3 & #4Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is swimming towards it at 3 m/sec. (net mv)before = (net mv)after (6 kg)(1 m/sec) + (2 kg)(-3 m/sec) = (6 kg + 2 kg)(vafter) 6 kg.m/sec + -6 kg.m/sec = (8 kg)(vafter) vafter = 0 m/sec

Now the 6 kg fish swimming at 1 m/sec swallows a 2 kg fish that is swimming towards it at 4 m/sec. (net mv)before = (net mv)after (6 kg)(1 m/sec) + (2 kg)(-4 m/sec) = (6 kg + 2 kg)(vafter) 6 kg.m/sec + -8 kg.m/sec = (8 kg)(vafter) vafter = -1/4 m/sec

MOMENTUM VECTORSMomentum can be analyzed by using vectorsThe momentum of a car accident is equal to the vector sum of the momentum of each car A & B before the collision.ABMOMENTUM VECTORS (Continued) When a firecracker bursts, the vector sum of the momenta of its fragments add up to the momentum of the firecracker just before it exploded.

The same goes for subatomic elementary particles. The tracks they leave help to determine their relative mass and type.