Energy and Transformation chemical fuel energy  vehicle motion electric energy  turning mixer, drill, etc. wind turbine  electrical energy  turn mixer

Energy: The work that a physical system is capable of doing in changing from its actual state to a specified reference state … (American Heritage Dictionary) Energy: The capacity to do work. (Physics) What is Work? Some Definitions

Work Work is force x distance. It takes energy to do work. Less stored energy is available after productive work is done.

Physics Definition of Work Work, W SI Unit: J = (N)(m) Work is the useful part of a force times the distance the object moves (“s”) “useful” means in direction of motion

Example of Work Work = Fcos  x = (80N)(cos40)(11m) = 674 J Given: F = 80N, Angle is 40°,  x is 11m,

Energy Kinetic, K: energy of motion K = ½mv 2. Ex: 2000kg car moving at 10m/s has kinetic energy of 100,000J. Potential, U: stored energy Ex: One gallon of gasoline stores 138,000,000J.

Work-Energy Theorem: The net work done on an object is equal to its change in Kinetic Energy. Example: The net work done on a 20kg mass is 250J. If the mass started from rest its final speed is 5m/s: ½(20)5 2 – 0 = 250.

Example A 20kg mass is moving at 5m/s. 250J of work (net) are done on it. What is its final speed?

A 20kg block slides across a floor. The frictional force on it is 50N. How much work is done on the block in moving 3m? If its initial speed was 5m/s, what is its speed after moving 3m?

A 20kg block is pushed with 75N of force. The frictional force on it is 50N. How much work is done on the block in moving 3m? If its initial speed was 5m/s, what is its speed after moving 3m?

How much work does a force perpendicular to an objects displacement do? Answer: Zero. The angle between F and s is 90, cos90 = 0.

The Dot Product

Example: A = (1, 1, 1), B = (5, 0, 0)

Example: Find the angle between A = (1, 1, 1) and B = (5, 0, 0)

2006 Ford Mustang Curb Weight: 3450 lbs. Performance Acceleration (0-60 mph): 5.1 sec. Braking Distance (60-0 mph): ft. Engine Type: V8 Horsepower: 300 hp

What size motor? Cube of bricks ~ 1 ton 1 ton = 2000 lbs ~ 9000 N Operating Speed: 10cm/s Minimum Power: P = Fv = (9000N)(0.1m/s) P = 900 W = 1.2 hp

Types of Energy Kinetic, K energy due to motion Potential, U energy due to position

Some Potential Energies Spring: Us Gravitational: Ug Thermal: Uth Chemical Uch We use the first three of these.

Springs Fs = -kx, Us = ½kx 2. k = “spring constant” in N/m and x is the change in length of the spring. Ex: A 100N/m spring is compressed 0.2m. It exerts (100N/m)(0.2m) = 20N of force. It stores ½(100N/m)(0.2m) 2 = 2J of energy.

Gravity F g = mg, U g = mgy Ex: A 2kg object experiences weight (2kg)(9.8N/kg) = 19.6N. At 3m above the floor it has a stored energy of (2kg)(9.8N/kg)(3m) = 48.8Nm = 48.8J.

Conservation of Energy Individual energy levels change. Sum of all individual energies is constant. Change in energy is called “work”

Energy Conservation Total Energy E = sum of all energies E =  K +  U example: t = 0: K = 0J, U = 4000J later: K = 2000J, U = 2000J

Conservation of Energy Example: Falling Ball KE increases U (gravitational) decreases E = K + Ug = constant

EnergyE1E2E3 Kinetic0½mv PE-g00mgh PE- spring ½kx 2 00 Totals  ½kx 2 ½mv 2 2 mgh

EnergyE(h)E(y) Kinetic0½mv 2 PE-gmghmgy Totals  mgh½mv 2 + mgy Energies and speeds are same at height y Accelerations at y are not same

EnergyEiEf Kinetic½mv i 2 0 PE-g00 Thermal0fksfks Totals  ½mv i 2 fksfks Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping. s

A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie- frame type diagram of the motion is shown below. TypeE1E2E3E4E5 gravita- tional mg(1)000mg(1/2) kinetic0½ m(v2) 2 0½ m(v4) 2 0 elastic00PE-elastic00 thermal00PE-thermal

By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J Calculate v2: (use 1st and 2nd columns) mg(1) = ½ m(v2)2. g = ½ (v2)2. v2 = 4.43m/s Calculate PE-thermal: (use 1st and 5th columns) mg(1) = mg(1/2) + PE-thermal mg(1/2) = PE-thermal PE-thermal = 9.8J

Calculate PE-elastic: (use 1st and 3rd columns) PE-elastic + PE-thermal = mg(1) PE-elastic = 19.6 PE-elastic = 9.8J Calculate v4: (use 1st and 4th columns) ½ m(v4)2 + PE-thermal = mg(1) ½ m(v4) = 19.6 ½ m(v4)2 = 9.8 (v4)2 = 2(9.8)/2 v4 = 3.13m/s

Terminology E: total energy of a system E-mech = total energy minus the thermal energy E-mech = E – U th.

Power: The time rate of doing work. SI Unit: watt, W = J/s] Example: How much average power is needed to accelerate a 2000kg car from rest to 20m/s in 5.0s? work =  KE

Horsepower: 1 hp = 746 watts For the previous example:

Another equation for Power: Ex: A car drives at 20m/s and experiences air- drag of 400N. The engine must use (400N)(20m/s) = 8,000 watts of engine power to overcome this force. 8,000 watts = 10.7 hp. What air drag force acts at 40m/s? How much hp is needed to overcome this drag?

What size electric motor is needed to raise 2000lbs = 9000N of bricks at 10cm/s? Minimum Power: P avg = Fv avg = (9000N)(0.1m/s) P = 900 W = 1.2 hp

An object moves in a vertical circle with constant mechanical energy. What does this imply about its speed?

A mass on a string moves in a horizontal circle. Does the tension in the string vary? Does the tension in the string do work on the mass?

Mechanical Advantage F1d1 = F2d2 (E conservation) F2/F1 = d1/d2 = mechanical advantage Example: A Jack moves a car 10cm upward with fifty 20cm strokes. Mechanical advantage is 50x20/10 = 100.