the time rate of doing work; or the time rate transfer of energy. Power, by definition, is the time rate of doing work; or the time rate transfer of energy. P = W / t Power is a scalar quantity.

1.0 J of energy is transferred The SI unit of power is the Watt, named in honor of James Watt. One Watt, W, of power is the power achieved when 1.0 J of work is done or 1.0 J of energy is transferred in a time of 1.0 s.

Power example An 80 kg human walks up a flight of stairs in .22 s that have an altitude gain of 3.75 m. What is the power of the person?

Power Example First find the work= force*distance. F=mg 80*9.8=784N W=Fd 784N*3.75m=2940J P=W/t=2940/.22=13363.64W

W = F·d Work, Work is a scalar quantity. by definition, is the product of the force exerted on an object and the distance the object moves in the direction of the force. W = F·d Work is a scalar quantity.

The SI unit of work is the Joule, named in honor of James Prescott Joule. One Joule, J, of work is the work done when 1.0 N of force is applied through a distance of 1.0 m.

Work Example An intern pushes a 75 kg patient on a 15 kg gurney, producing an accleration of .06m/s2. How much work does the intern do by pushing the patient and gurney through a distance of 2.5 m? Assume there is no friction.

Find the F= ma 15+75=90 kg* .60 m/s2 F= ma 90*.6= 54N W=Fd= 54*2.5=135J

“Force vs. Displacement” graph. Graphically, work is the area under a “Force vs. Displacement” graph. displacement, m

work = Fd(cosq), W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J If the force and displacement are not in the exact same direction, then work = Fd(cosq), where q is the angle between the force direction and displacement direction. F =40 N d = 3.0 m Example 2:The work done in moving the block 3.0 m to the right by the 40 N force at an angle of 35 to the horizontal is ... W = Fd(cos q) = (40N)(3.0 m)(cos 35) = 98 J

Law of Conservation of Energy “Energy can be neither created nor destroyed. It may only change forms.” S all types of energy before the event = S all types of energy after the event Examples: A dropped object loses gravitational PE as it gains KE. A block slides across the floor and comes to a stop. A compressed spring shoots a ball into the air.

Energy comes in many forms: mechanical, electrical , magnetic, solar, the ability (capacity) to do work Energy comes in many forms: mechanical, electrical , magnetic, solar, thermal, chemical, etc... The SI unit of energy is the Joule. Energy, like work, is a scalar.

KE = 1/2 mv2 Kinetic Energy energy of motion All moving objects that have mass have kinetic energy. KE = 1/2 mv2 m - mass of the object in kg v - speed of the object in m/s KE - the kinetic energy in J

Energy Example A 50 kg boy and his 100 kg father went jogging. Both ran at a rate of 5 m/s. Who had more kinetic energy? Show your work and explain.

Example Problem - answer KE = ½mv2 Boy… KE = ½(50 kg)(5 m/s)2 KE = 625 J Dad… KE = ½(100 kg)(5 m/s)2 KE = 1250 J Dad had more Kinetic energy because his mass was greater.

Work-Energy Theorem the net work done on an object is equal to its change in kinetic energy

Potential Energy Energy stored in a motionless object, giving it the potential to cause change

Potential Energy energy of position or condition Chemical Potential Energy - energy stored in chemical bonds between atoms (Snickers bar, food, even gasoline)

PEg = mgh Potential Energy energy of position or condition gravitational potential energy PEg = mgh m - mass of object in kg g - acceleration of gravity in m/s2 h - height of object, in m, from some arbitrary reference point PE – gravitational potential energy in J

Example Problem What is the potential energy of a 10 N book that is placed on a shelf that is 2.5 meters high?

Example Problem - answer GPE = mgh GPE = (10 N) (2.5m) GPE = 25 J Remember that weight = mg and that the force provided is weight. NOTE: you may want to change your variable for weight to Fg.

PEe = ½ kx2 Potential Energy energy of position or condition elastic potential energy PEe = ½ kx2 k – elastic constant in N/m x - elongation or compression in m PEe – elastic potential energy in J Click here to investigate elastic constants.

Example A spring with a spring constant of 120 N/m is compressed a distance of 2.3 cm. How much potential energy is stored in the spring?

Example U= ½ kx2 U= ½ (120)*(.025)2 Remember we work in meters! U= .032J