Conservation of Mechanical Energy

Mechanical Energy

»Mechanical energy is the energy that is possessed by an object due to its motion or due to its position. Mechanical energy can be either kinetic, potential or the combination.

» »ME total = PE + KE

Mechanical Energy

» Some forces will change the total mechanical energy of the object.

» And some forces will NOT change the total mechanical energy of an object, but instead can only transform the energy of an object from potential energy to kinetic energy (or vice versa).

» Our tennis ball lab demonstrated this principle...

Example: Conserved Energy

» The diagram below demonstrates a ski jump of Li Ping Phar (esteemed Chinese ski jumper) as she glides down the hill and makes one of her record-setting jumps.

Example: Conserved Energy

» The total mechanical energy of Li Ping Phar is ME total = PE + KE = 50,000 J

» Notice that ME total = constant throughout her motion.

Internal vs. External Forces

» There are conditions under which the ME total will be a constant value and conditions under which it will be a changing value.

» We can categorize forces based upon whether or not their presence is capable of changing an object's total mechanical energy.

Internal vs. External Forces

» Internal forces = Conservative Forces » Gravity» electrical forces» magnetic forces» spring forces» When an internal force is applied, the MEtotal of

that object remains constant, but the object's energy changes form.

» MEf = ME0

»

Internal vs. External Forces

» For example, as an object is "forced" from a high elevation to a lower elevation by gravity, some of the potential energy is transformed into kinetic energy.

» The sum of the kinetic and potential energies remains constant.

» This is referred to as energy conservation. » Because internal forces do not change MEtotal,

they are called conservative forces. They conserve mechanical energy.

Internal vs. External Forces

» External forces = Non-conservative Forces (forces due to contact b/w objects) include

» applied force» normal force» tension force» friction force» air resistance force. » When an external force is applied, the MEtotal is

changed.

Internal vs. External Forces

» If the work is positive work, then the object will gain energy.

» If the work is negative work, then the object will lose energy.

» » The gain or loss in energy can be in the form of

potential energy, kinetic energy, or both. »

Internal vs. External Forces

» The work that is done, W = ΔMEtotal = MEf – ME0

» Because external forces are capable of changing the total mechanical energy of an object, they are referred to as non-conservative forces.

Internal vs. External Forces

» MEtotal = PE + KE i.e., the total mechanical energy at any moment

» Wexternal = MEfinal - ME0 i.e., the total WORK done by external non-conservative forces

» Wexternal = [KEfinal + PEfinal ] - [KE0 + PE0]

» » This is often re-written as "the initial energy +

the work done = final energy".» ME0 + Wexternal = MEfinal

Example

» EX: A weightlifter applies an upwards force of 1000 N to a barbell to displace it upwards a given distance = 0.25 m at a constant speed. The barbell begins with 1500 Joules of potential energy because it is resting on a rack above the gym floor, approximately at chest-level of the weightlifter.

» How much work does the weightlifter apply?

» F•d•cos θ= 1000 • 0.25 = 250 J» How much energy does the barbell have once

he has lifted the barbell? » 1500 J+ 250 J = 1750 J.»

Example

» In what form (PE or KE or both) is the final energy?

» The barbell began with potential energy. KE was added to the bar by lifting it (external force) and then this was changed into PE. The final energy is all PE.

Example

» EX: Now consider a car that is skidding from a high speed to a lower speed.

» The force of friction between the tires and the road exerts a leftward force = 8000 N.

» The car moves rightward 30 m.» The car begins with 320 000 Joules of energy.» How much work does the Friction Force do?» (F•d•cosθ = 8000 •30• cos(180) = -240 000 J»

Example

» How much energy does the car finish with?» 320,000 + (-240,000) = 80,000.» The car finishes with 80, 000 Joules of

mechanical energy. » In what form (PE or KE or both) is the final

energy? » The car began with KE. KE was removed from

the car by friction (external force). There was no change in height so no change in PE. The car is still in motion at the end of the scenario; all ME is KE.

»

Work - Energy

» In both examples, an external force does work upon an object over a given distance to change the total mechanical energy of the object.

» If the external force (nonconservative force) does positive work, then the object gains mechanical energy. The amount of energy gained is equal to the work done on the object.

» .

Work - Energy

» If the external force (nonconservative force) does negative work, then the object loses mechanical energy. The amount of mechanical energy lost is equal to the work done on the object.

» The work-energy relationship can be combined with the expressions for potential and kinetic energy to solve complex problems.

» W= ∆ME = FdcosƟ

Assignment

» P. 187 Focus #13» P. 190 #37-45odd; 51-57odd» For #37, you will need to use kinematics

to find v2

» For #45, you will need to start with kinematics to find v at the bottom of the slide, and to find h (the height of the bottom of the slide from the water).