Post on 14-Jan-2016
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
sFW )cos(
Example of Work
Work = Fcosx = (80N)(cos40)(11m) = 674 J
Given: F = 80N, Angle is 40°, x is 11m,
Energy
• Kinetic, K: energy of motionK = ½mv2.
• 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.
2212
21
ifnet mvmvW
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)52 – 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
zzyyxx BABABABA
Example: A = (1, 1, 1), B = (5, 0, 0)
5)0)(1()0)(1()5)(1( BA
Example: Find the angle between A = (1, 1, 1) and B = (5, 0, 0)
5)0)(1()0)(1()5)(1( BA
cosABBA 3111 222222 zyx AAAA
5005 222222 zyx BBBB
cos535
7.54
3/153/5cos
FFsFW 4)0,3,4)(0,0,(
JsFW 14)0,5,2)(0,4,3(
2006 Ford MustangCurb Weight: 3450 lbs. Performance Acceleration (0-60 mph): 5.1 sec. Braking Distance (60-0 mph): 121.37 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 = ½kx2.
• 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
• Fg = mg, Ug = 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
Energy E1 E2 E3
Kinetic 0 ½mv22 0
PE-g 0 0 mgh
PE-spring
½kx2 0 0
Totals
½kx2 ½mv22 mgh
Energy E(h) E(y)
Kinetic 0 ½mv2
PE-g mgh mgy
Totals mgh ½mv2 + mgy
Energies and speeds are same at height y
Accelerations at y are not same
Energy Ei Ef
Kinetic ½mvi2 0
PE-g 0 0
Thermal 0 fks
Totals ½mvi2 fks
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.
Type E1 E2 E3 E4 E5
gravita-tional
mg(1) 0 0 0 mg(1/2)
kinetic 0 ½ m(v2)2 0 ½ m(v4)2 0
elastic 0 0 PE-elastic 0 0
thermal 0 0 PE-thermal PE-thermal PE-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-thermalPE-thermal = 9.8J
Calculate PE-elastic: (use 1st and 3rd columns)PE-elastic + PE-thermal = mg(1)
PE-elastic + 9.8 = 19.6PE-elastic = 9.8J
Calculate v4: (use 1st and 4th columns)½ m(v4)2 + PE-thermal = mg(1)
½ m(v4)2 + 9.8 = 19.6½ 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 – Uth.
Power: The time rate of doing work.
SI Unit: watt, W = J/s]time
workPavg
Example: How much average power is needed to accelerate a 2000kg car from rest to 20m/s in 5.0s?
work = KE 2212
21
if mvmv 2
212
21 )/0)(2000()/20)(2000( smkgsmkg
J000,400
s
J
t
workPavg 0.5
000,400 watts000,80
hpwatt
hpwatts107
746
1000,80
Horsepower: 1 hp = 746 watts
For the previous example:
avgavg vFt
sF
t
sF
t
WP )(cos)(cos
)(cos
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:
Pavg = Fvavg = (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.