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
Forces are vectors You can consider perpendicular motion independently. F=ma means: F x (total) = ma x F y (total) = ma y or: F (total) = m a y x F y F x F
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 = mc 2
where c is the speed of light. The speed of light is equal to c = 3 10 8 meters/second .
1. A ball with mass of 0.01 kg traveling at 100 km/hour.
First convert v=100 km/hour to v=100,000 m/hour x 1hour/3600 sec=28 meters/sec
then, E = 0.5 x 0.01 x (28) 2 Joules
E = 3.9 Joules
2. An asteroid, 10 km in diameter, with mass of 1x10 13 kg traveling at 15 km/sec.
First convert v=15 km/sec = 15,000 meters/sec
E = 0.5 x 10 13 x (15,000) 2 Joules
E = 1.1x10 21 Joules
Convert to kilotons of TNT
E = 1.1x10 21 Joules x (1 kiloton/4.184x10 12 Joules)
E = 2.7x10 8 kilotons of TNT
The atomic bomb dropped on Hiroshima released and energy of 15 kilotons
Gravitational Potential Energy: E = mgh h = height g = * 9.82 m/s 2 m = mass * On Earth
Example of Potential Energy Cheryl Haworth lifts 297.6 lbs a distance of 2 meters m = 297.6 lbs x 0.453 kg/lbs = 135 kg mg = 135 kg x 9.8 m/s 2 = 1.3 10 3 Newtons E=mgh = 1.3 10 3 N x 2 m= 2.6 10 3 Joules E= 2.6 10 3 Joules (1 Cal/4186 J) E = 0.63 Calories !!
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/sec 2 . Last class we showed that the velocity gained after traveling a distance d is given by The kinetic energy is then
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.
Summary Energy exists in many forms, for example in motion, the separation of masses, the separation of charges, mass… We will work mainly with potential energy and kinetic energy in this class. In a closed system, energy is conserved. This principal allows us to predict motion with out dealing with vectors.
James Prescott Joule (1818-1889) Joule determined the mechanical equivalent of heat by measuring change in temperature produced by the friction of a paddlewheel attached to a falling weight in the 1840s. He made a series of measurements and found that, on average, a weight of 772 pounds falling through a distance of one foot would raise the temperature of one pound of water by 1° F. This corresponds to (772 ft lbs)(1.356 J/ft lb) = 59 453.6 Calories, or 1 cal = 4.15 Joules, in close agreement with the current accepted value of 1 calorie = 4.184 Joules. The son of a prosperous brewer in North England, Joule financed his experiments himself.