Work, Energy and Power!Work, Energy and Power!

The Calculations and Equations

James JouleJames Joule

• British physicist James Joule is best British physicist James Joule is best known for his work in electricity and known for his work in electricity and thermodynamics Together with the thermodynamics Together with the physicist William Thomson (later Baron physicist William Thomson (later Baron Kelvin), Joule found that the Kelvin), Joule found that the temperature of a gas falls when it temperature of a gas falls when it expandsexpands without doing any work. This without doing any work. This principle, which became known as the principle, which became known as the Joule-Thomson effect, underlies the Joule-Thomson effect, underlies the operation of common refrigeration and operation of common refrigeration and air conditioning systems.air conditioning systems.

• The metric system The metric system unit of energyunit of energy is the is the joule (J), after James Joule.joule (J), after James Joule.

MechanicalMechanical

• Mechanical energyMechanical energy is the energy which is the energy which is possessed by an object due to its motion is possessed by an object due to its motion or its stored energy of positionor its stored energy of position• Kinetic energy :Kinetic energy : is the energy of motion is the energy of motion• Potential EnergyPotential Energy : : an object can store energy an object can store energy

as the result of its position or elastic source as the result of its position or elastic source

Work ConceptWork Concept

• WorkWork is defined as a force acting upon an is defined as a force acting upon an object to cause a displacement object to cause a displacement

• Mathematically, work can be expressed by Mathematically, work can be expressed by the following equation.the following equation.

• W= F x d cos W= F x d cos cos 0 cos 000 = 1) = 1)

• where F = force, d = displacement, and the where F = force, d = displacement, and the angle (theta) is defined as the angle between angle (theta) is defined as the angle between the force and the displacement vectorthe force and the displacement vector

Work CalculationsWork Calculations

W=F x d W=F x d cos 300 W= F x d

=100N X 5m = 100N X 5m X .87 =15Kg(10m/s2) X 5m

=500 N m = 413 N m = 750 N m

Gravitational Potential EnergyGravitational Potential Energy

• After an object has been lifted to a After an object has been lifted to a height, work is done.height, work is done.

• PE = W= F x d= mahPE = W= F x d= mahPotential Energy is maximum at the maximum HEIGHT

Potential Energy CalculationPotential Energy Calculation

• How much potential energy is lost by a How much potential energy is lost by a 5Kg object to kinetic energy due a 5Kg object to kinetic energy due a decrease in height of 4.5 mdecrease in height of 4.5 m

• PE = mahPE = mah• PE = (5Kg)(10 m/sPE = (5Kg)(10 m/s22)(4.5 m))(4.5 m)• PE = 225 Kg mPE = 225 Kg m22/s/s2 2

• PE = 225 JPE = 225 J

Kinetic Energy CalculationKinetic Energy Calculation

• The energy of motionThe energy of motion KE = W= F x d= mah=1/2 mvKE = W= F x d= mah=1/2 mv22

• Find the kinetic energy of an 4 Kg object Find the kinetic energy of an 4 Kg object moving at 5m/s.moving at 5m/s.

• KE = 1/2 mvKE = 1/2 mv22

• KE = ½ (4Kg)(5m/s) KE = ½ (4Kg)(5m/s) 22

• KE = 50 Kg m KE = 50 Kg m 22 /s /s 22

• KE = 50 JKE = 50 J

Elastic potential energy Elastic potential energy

Spring constant CalculationSpring constant Calculation

A tired squirrel (mass of 1 kg) does push-ups by applying a force to elevate its center-of-mass by 5 cm. (A) Determine the number of push-ups which a tired squirrel must do in order to do a mere 5.0 Joules of work. (B) Determine the squirrel’s spring constant.

Spring Constant CalculationSpring Constant Calculation

• W = F x d = 10 N*(.05m)=.5 N m W = F x d = 10 N*(.05m)=.5 N m • W = .5 J (each push up)W = .5 J (each push up)• 10 pushups = 5 J10 pushups = 5 J• PE = ½ k x PE = ½ k x 22

• .5 J = ½ k (.05m) .5 J = ½ k (.05m) 22

• .5 J = ½ k (.003m .5 J = ½ k (.003m 22))• .5 J = .0015 m .5 J = .0015 m 2 2

• 333.3 J/m 333.3 J/m 2 2 = k= k

Power!Power!

• Power is the rate that we use energy.Power is the rate that we use energy.• Power = Work or Energy / TimePower = Work or Energy / Time• P = W/t = F x d/t = F vP = W/t = F x d/t = F v• The units for power :The units for power :

• J/sJ/s• Kg mKg m22 / s / s2 2 /s/s• N m / sN m / s

Power CalculationPower Calculation

• A 5 Kg Cart is pushed by a 30 N force A 5 Kg Cart is pushed by a 30 N force against friction for a distance of 10m in 5 against friction for a distance of 10m in 5 seconds. Determine the Power needed to seconds. Determine the Power needed to move the cart.move the cart.

• P = F x d / tP = F x d / t• P = 30 N (10 m) / 5 sP = 30 N (10 m) / 5 s• P = 60 N m /sP = 60 N m /s• P = 60 wattsP = 60 watts

SummarySummary

• Energy is the ability to moveEnergy is the ability to move• Potential is stored energy (Statics)Potential is stored energy (Statics)

• Dependant on heightDependant on height

• Kinetic is moving energy (Dynamics)Kinetic is moving energy (Dynamics)• Dependant on velocityDependant on velocity

• Springs store energy dependant on distance Springs store energy dependant on distance and constantand constant