ISNS 3371 Phenomena of Nature Energy Comparisons Solar

ISNS 3371 - Phenomena of Nature Energy �Comparisons Solar energy striking Earth’s surface per second = 2. 5 x 1017 J. Energy released by burning 1 liter of oil = solar energy striking square 100 m on a side in 1 second

ISNS 3371 - Phenomena of Nature Fundamental Forces of Nature Four Types of Forces: • Gravitational – holds the world together • Electromagnetic – attraction/repulsion of charged matter • Strong Nuclear – holds nucleus together • Weak Nuclear – involved in reactions between subatomic particles

ISNS 3371 - Phenomena of Nature Energy Three basic categories: Mechanical Energy { Kinetic energy = energy of motion KE = 1/2 mv 2 Potential energy = stored energy gravitational, chemical, elastic, electrostatic, etc… Radiative - energy carried by light

ISNS 3371 - Phenomena of Nature Potential Energy One form of potential energy is gravitational potential energy - the energy which an object stores due to its ability to fall • It depends on: – the object’s mass (m) – the strength of gravity (g) – the distance which it falls (h) g m PE = mgh h Before the sun was formed - matter contained in cloud diffuse gas cloud - most far from the center - large gravitational energy. As cloud contracted under its own gravity - gravitational energy converted to thermal energy until hot enough to ignite nuclear fusion

ISNS 3371 - Phenomena of Nature Potential Energy • energy is stored in matter itself • this mass-energy is what would be released if an amount of mass, m, were converted into energy E = mc 2 [ c = 3 x 108 m/s is the speed of light; m is in kg, then E is in joules] The mass energy in a 1 -kg rock is equal to as much energy as 7. 5 billion liters of oil = enough to run all the cars in the U. S. for a week A 1 -megaton hydrogen bomb converts only about 3 ounces of mass into energy.

ISNS 3371 - Phenomena of Nature Conservation of Energy • Energy can be neither created nor destroyed. • It merely changes it form or is exchanged between objects. • This principle (or law) is fundamental to science. • The total energy content of the Universe was determined in the Big Bang and remains the same today.

ISNS 3371 - Phenomena of Nature Types of Energy cannot be created or destroyed, only changed – Mechanical – • Potential - stored energy • Kinetic- energy of motion KE=1/2 mv 2 – Electrical – Chemical – Elastic – Gravitational – Thermal – Radiant – Nuclear

ISNS 3371 - Phenomena of Nature Conversion of Energy Throwing a baseball Nuclear energy (nuclear fusion on sun) - Radiative energy (sunlight) - Chemical energy (photosynthesis) - Chemical energy in pitcher’s body (from eating plants) - Mechanical kinetic energy (motion of arm) - Mechanical kinetic energy (movement of the baseball). Thus, ultimate source of KE in baseball is mass energy stored in hydrogen of Sun - created in Big Bang. Hydroelectric dam Gravitational - mechanical - electrical Nuclear reactor Nuclear - thermal - mechanical - electrical Car Chemical - thermal - mechanical

ISNS 3371 - Phenomena of Nature Power: Rate of change of energy Power = work done/time interval = E/ t (remember: means a change in a quantity) Power: 1 watt = 1 J/s Thus for every second a 100 W light bulb is on, the electric company charges for 100 J of energy. The average daily power requirement for a human is about the same as for a 100 -W light bulb.

ISNS 3371 - Phenomena of Nature Applications of Conservation of Energy

ISNS 3371 - Phenomena of Nature Machines can be used to multiply force: (force X distance)input = (force X distance)output Decrease the distance and the force will increase. Work/Energy is not changed!

ISNS 3371 - Phenomena of Nature Levers Fulcrum is in the center: d 1 = d 2 so F 1 = F 2 Fulcrum is closer to one end: d 1 > d 2 So F 2 > F 1 Give me a long enough lever and a place to put the fulcrum and I can move the world (Archimedes, 250 BC).

ISNS 3371 - Phenomena of Nature Pulleys

ISNS 3371 - Phenomena of Nature Pendulum solution (you are not expected to know this) For small angles, sin = This becomes the differential equation: vt, at r = vt/r is the angular velocity = at/r is the angular acceleration so = r With solution For a complete oscillation: so

ISNS 3371 - Phenomena of Nature For a small pendulum clock, P = 1 s So If P = 2 s, then l = 0. 993 m This is the length of the typical grandfather clock’s pendulum which advances each time the pendulum reaches its maximum displacement or twice every period.

ISNS 3371 - Phenomena of Nature Objects Moving Down an Inclined Plane Compare the speed of an object rolling down an inclined plane without slipping and one sliding without friction. Which gets to the bottom first? We simulate this with two cylinders of the same mass - one is a solid cylinder, and one has wheels on the sides which turn while the cylinder itself doesn’t. The sliding object will always reach the bottom first because all the initial potential energy is converted into translational energy with none wasted in rotation.

ISNS 3371 - Phenomena of Nature Which will roll down the inclined plane faster - a solid cylinder or a hollow cylinder (of the same mass and outer radius)? As the object rolls down the plane, its initial potential energy is converted into both translational energy of the center-of-mass and also into rotational energy. - ratio of rotational to translational energy is I / mr 2 where I is the moment of inertia, m is the mass and r is the radius of the object. - moment of inertia is mr 2/2 for the solid cylinder and m(r 12 + r 22)/2 for the hollow cylinder. - Since r 2 of the hollow cylinder is equal to r of the hollow cylinder, and the mass is the same, the moment of inertia of the hollow cylinder is mr 12/2 + mr 2/2 or larger than the moment of inertia of the solid cylinder by mr 12/2. Thus ratio of the rotational to the translational energy for the hollow cylinder is greater than for the hollow cylinder. The hollow cylinder therefore acquires the most rotational energy and the least translational energy (and velocity) and thus takes the longest to get down the plane.

ISNS 3371 - Phenomena of Nature Using Conservation of Energy and Momentum to Calculate the Velocity of Two Bodies After a Collision Conservation of momentum says (1) Conservation of energy says (2) (1) Can be written (1 a) (2) Can be written (2 a) From (1 a) we see that m 1(v 1 - V 1) cancels out m 2(V 2 - v 2) so that Which can be rewritten as

ISNS 3371 - Phenomena of Nature Substitute V 1 = V 2 + v 2 - v 1 into (1) This leaves us with one equation with one unknown, V 2 Similarly

ISNS 3371 - Phenomena of Nature The Ballistic Pendulum The ballistic pendulum is used to determine the speed of a projectile. Invented in the 18 th century by Benjamin Robins to determine the speed of a bullet. A bullet of mass m is fired at a block of wood (mass M) hanging from a string. The bullet embeds itself in the block, and causes the combined block plus bullet system to swing up a height h. Conservation of momentum and conservation of energy are used to determine the bullet’s speed.

ISNS 3371 - Phenomena of Nature Conservation of momentum (1) b = before collision- mb and vb are for the ball/bullet a = after collision- ma and va are for the ball/bullet and pendulum Conservation of energy Kinetic Energy of ball and pendulum just after collision = Potential Energy of ball and pendulum at end of swing: h = height of pendulum at end of swing Substitute into (1):

ISNS 3371 - Phenomena of Nature Alternate Way Using Projectile Motion and g Fire ball from top of table. Measure initial height of ball (h) and horizontal distance traveled (x). h x Vertical motion (1) Horizontal motion Substitute from (1)