Work & Energy "There is nothing new to be discovered in physics now, All that remains is more and more precise measurement.” -Lord Kelvin “Time is nature’s way of making certain that everything doesn't happen all at once.” -Woody Allen

Importance of Numbers Debt: 9.2 x 1012 $

Work & Energy W = F x d Work = Force x distance A force is required to accelerate a body. The exertion of a force over a distance is called work. This requires energy. W = F x d Work = Force x distance

Work W = F x d Cheryl Haworth lifts 297.6* lbs a distance of 2 meters. How much work does she do? W = F x d d = 2 m F = m* x a = m x g = 135 kg x 9.8 m/s2 W = F x d = m x g x d = 135 kg x 9.8 m/s2 x 2 m = 2657 Joules = 2657 Joules  (1 Cal/4186 J) = 0.635 Calories *A mass of 135 kg causes a gravitational force of 297.6 lbs on the surface of Earth

Energy Energy is required to do work. The energy added to the object equals the work done. Energy required to move something a distance against gravity is called gravitational potential energy

Gravitational Potential Energy: E = W = F x d = (m x g) x h h = height g = * 9.82 m/s2 m = mass e.g. E = 1000 m * 70 kg * 9.82 m/s2 = 6.87x105 Newton meter * On Earth’s surface

Energy & Work Units Energy is measured in different units. The most common are: Joules (J) = Newton-meter (F x d) *Calories (Cal) = 4186 J Foot-pounds (ft-lbs) = 1.356 J British Thermal Units (BTU) = 1055 J Kiloton of TNT = 4.184x1012 J Calories with a small “c”, cal = Cal/1000. All foods are listed as big C calories or kilocalories (in Europe)

Potential Energy Cheryl Haworth lifts 297.6* lbs a distance of 2 meters. How much energy did the bar gain? E = W = F x d E = F x d = m x g x d = 135 kg x 9.8 m/s2 x 2 m = 2657 Joules = 2657 Joules  (1 Cal/4186 J) = 0.635 Calories *A mass of 135 kg causes a gravitational force of 297.6 lbs on the surface of Earth

Some Kinds of Energy Kinetic Energy – the energy of moving objects. This energy is: E = (1/2) m v2 Heat, or thermal energy – of warm bodies. Chemical Energy – of chemical reactions (involving electrons) Gravitational Potential Energy – of a gravitational field. E = m g h Electromagnetic Energy – energy associated with electric & magnetic forces. Mass Energy – all objects have energy by virtue of their mass, the energy released in nuclear explosions, involving nuclei.

Why discuss Energy? It is transferable and conserved.

Kinetic Energy E = 1/2 mv2 E = energy (Joules) m = mass (kilograms) v = speed (meters/sec.) Example: Griffith-Joyner runs 100 m in 10.61 seconds. What is her Kinetic Energy? Her mass was 60 kg and height 5’ 6’’ Florence Griffith-Joyner (born Delorez Griffith) sprints to the finish line 1 Joule = 1 kg meter2/second2

Kinetic Energy E = 1/2 mv2 E = energy (Joules) m = mass (kilograms) v = speed (meters/sec.) Example: Griffith-Joyner runs 100 m in 10.61 seconds. What is her Kinetic Energy? Her mass was 60 kg and height 5’ 6’’ v = d/t = 100/10.61 = 33.93 m/s E = 0.5 * 60 kg * (33.93 m/s)2 = 34,500 Joules = 3.4 x 104 Joules Florence Griffith-Joyner (born Delorez Griffith) sprints to the finish line 1 Joule = 1 kg meter2/second2

Another Kinetic Energy Example A ball with mass of 0.5 kg is dropped from a distance of 10 meters. What is its kinetic energy when it hits the floor? We know that the ball falls towards the Earth with a constant acceleration of 9.8 meters/sec2. Last class we showed that the velocity gained after traveling a distance d is given by The kinetic energy is then

Potential Energy Example A NATS102 professor lifts a ball with mass 0.5 kg a height of 10 meters. How much potential energy does the ball gain? W = mah = 0.5  9.8  10 = 49 Joules But this is the same as the kinetic energy the ball gained by falling 10 meters. What’s going on???

Kinetic Energy Examples A ball with mass of 0.01 kg traveling at 100 km/hour. What is its Kinetic Energy? First convert v=100 km/hour to unit of meter/sec: Note 100 km = 100x1000 m = 100,000 m Note 1 hr = 3600 seconds Thus: v=100,000 m/hour x 1hour/3600 sec=28 meters/sec And: E = 0.5 x 0.01 x (28)2 Joules E = 3.9 Joules

A more interesting example 2. An asteroid, 10 km=10,000 m in diameter, with a density of 3000 kg/m3, traveling at 30 km/sec. What is its Kinetic Energy? First: what is the asteroid’s mass? mass = density x volume mass = density x (4/3)  R3 where R = radius = (1/2) diameter Compare your answer to the energy of that of 15 kilotons of TNT, which is the energy of the atomic bomb dropped on Hiroshima.

Mass and Energy One of Einstein’s many contributions was the recognition that mass is simply another form of energy. Mass and other forms of energy can be interchanged, as can kinetic energy, potential energy, heat, etc. The amount of energy contained in an object with mass m is given by the famous equation E = mc2 where c is the speed of light. The speed of light is equal to c = 3108 meters/second.

The energy of a NATS102 Student A NATS102 student has a mass of 80 kg (weight of 170 lbs). According to Einstein’s equation, he/she has an energy of E = mc2 = 80 kg (3108 m/s)2 Joules E = 7.21018 Joules convert to kilotons of TNT E = 7.21018 J x (1 kton/4.1841012 J) =1.71018 kilotons This is enormous. The tremendous amount of energy contained in matter is the reason for the power of nuclear bombs, reactors, stars, supernovae, etc.

Conservation of Energy Energy is neither created nor destroyed but only transformed from one form to another. In a closed system, the total amount of energy is conserved. If we add up the amount of energy in a closed system including all of the different forms, the sum will not change with time. The total amount of energy never changes, it only moves from place to place and from one form to another. Conservation of Energy applies not just to kinetic and potential energy, as in the example, but to all kinds of energy (heat, chemical, …)

Conservation Laws in Physics Conservation laws are powerful tools Most fundamental quantities (mass, energy, & momentum) satisfy conservation laws. Conservation laws are easy – no vectors

Conservation of Energy m = 50.9 kg

Power The rate of doing work or expending energy P = Energy/Time Rock climbers gain a lot of potential energy but do so slowly, at low power

Lance training in Arizona Power Training Cyclists do work more quickly than rock climbers. They expend more power. Lance Armstrong expends about 10,000 Calories in a 2 hour race. This corresponds to a power of roughly 6 kilowatts. Racing: Tour de France Lance training in Arizona

Niagara Falls 570,000 kg of water descend every second. The falls height is 55 meters. Thus the potential energy of 1 kg of water is E=mha=19.855 J = 539 J. The total power is then P=570,000539 Joules/sec=3.1108 Watts or 310 Megawatts.

Climbing out of the Grand Canyon How big a lunch is needed? Energy from lunch = Work to be done W = mgh = (62 kg)(9.82m/s2)(1500 m) = 9.1x105 Joules = 218 Calories That is, 1 peach & a glass of milk That’s it?

Nope – we’re inefficient Humans work at roughly 15% efficiency. The rest of the energy goes into heat and non-work productive movement. So, to climb the Grand Canyon, we need 1450 Cal ! Two club sandwiches, one egg, 1 fruit and 1 glass of milk.

A more interesting example 2. An asteroid, 10 km=10,000 m in diameter, with a density of 3000 kg/m3, traveling at 30 km/sec. What is its Kinetic Energy? First: what is the asteroid’s mass? mass = density x volume mass = density x (4/3)  R3 v=30 km/sec = 30,000 meters/sec E = 0.5 x 1x1013 x (30,000)2 Joules E = 4.5x1021 Joules Convert to kilotons of TNT E = 4.5x1021 Joules x (1 kiloton/4.184x1012 Joules) E = 2.2x108 kilotons of TNT The atomic bomb dropped on Hiroshima released and energy of 15 kilotons