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Energy: Basics. Definitions. Energy - the ability to do work. Work - the transfer of energy by applying a force through a distance. But what is a “force”?. Position.
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Definitions Energy - the ability to do work Work - the transfer of energy by applying a force through a distance But what is a “force”?
Position Position - orientation and distance an objectis from some origin; measurement of position requires a coordinate system If the position does not change, the object is easily found Displacement - change in position; if position is designated with the vector r, then displacement is Dr
Velocity Defn. - time rate of change ofdisplacement; is a vector quantity; SI unit = m/s Displacement Dr Average velocity = = Elapsed time Dt Instantaneous velocity = limit (average velocity) Dt0 What is the average velocity of a dragster that takes 5.5 secondsto go the 400 meters down the dragstrip?
Speed Some books say that velocity is speed + direction. WRONG! Distance traveled Average speed = Elapsed time Displacement = Distance traveled Displacement on racetrack is 0, while distance travelled is not
Acceleration Defn. - time rate of change of velocity;is a vector quantity; SI unit ism/s2 Dv Average acceleration = Dt Accelerations can occur without changing the magnitude of velocity; Ex. Object going in circle at constantrate
Newton’s First Law Really, Galileo’s “An object at rest, or in a state of constant motion, will continue in that state unless acted upon by an unbalanced force.” Inverse of statement is very important: if an object is acceleration, then a net force is operating on it, even if you cannot see the reason for the force. Is there a force operating in this picture,and if so, from what direction?
Newton’s Second Law F = ma Relates kinematic variables to dynamic ones Can measure accelerations calculate forces Note: SI unit is newtons, English is poundsIncorrect to say that X pounds = Y kilograms Not all forces are constant What force is needed to accelerate a 1000 kg car to 5 m/s2?
Newton’s Third Law “For every force, there is an equal and opposite reaction force.” Often misunderstood; actually means that one object actingon a second object will have the second object act on it Mule pulls on cart. Cart pulls back onmule with equal and opposite force.“Why pull?”, says mule, if force willbe negated.
Get Back To Work Work - the transfer of energy by applying a force through a distance W = F x d if F is constantDW = Fn x Dd if F varies Lifting box: F = mgDistance lifted = h W = mg x h = mgh
Work Example How much work is done by lifting a 10 kgbox 2 meters from the floor to a shelf?m = 10 kg h = 2 m Lifting box: F = mg = (10 kg)(9.8 m/s2) = 98 NDistance lifted = h = 2 m W = mg x h = (98 N) (2 m) = 196 J
TYPES OF POTENTIAL ENERGY: Gravitational Chemical Nuclear Potential energy Energy stored within the force between two objects separated by a distance; if objects are allowed to move, force is applied through distance = work done
EXAMPLES: Water behind a dam A rock at the top of a steep hill Example: Gravitational potential energy Potential energy due to gravity If the water or rock drops, gravity operates over a distance, thereby doing work. This work converts the potential energy to kinetic energy.
ENERGY OF MOTION A moving object has momentum. If it hits another object, it will transfer energy to it by applying a force through a distance, i.e. work Kinetic energy Some of the bullet’s kinetic energy is transferred to the apple during the collision Kinetic energy of falling water is converted to motion of turbines when water falls on them
Kinetic Energy (cont.) The kinetic energy of an object depends onlyon its mass and its velocity K.E. = ½ m v2 Example: A .03 kg bullet is moving at 300 m/s right before it hitsan apple. How much kinetic energy does it have? K.E. = ½ (.03 kg) (300 m/s)2 = (.015 kg)(90000 m2/s2) = 1350 J
Energy from chemical bonds is converted to kinetic energy and heat (body and friction from tires) ENERGY Heat 1st law of thermodynamics Energy may be converted to different forms, but it is neither created nor destroyed during transformations Amount of energy before and after transformation is the same, only the form of the energy has changed
1st Law (Contd.) Example: Can make wood hotter by applying fire or hitting Another way to state the 1st law is mathematically. DE = Q + W This equation says that the only way to change the energy of a system is to add heat to it (Q) or to do work on it (W)
Conservation of Energy If no external work is done on a system, or ifno heat is exchanged with its surroundings, then the total energy of a system will not change, i.e. the total kinetic plus the total potential energy will remain constant Energy can be converted from one form to the other (potential to kinetic or vice-versa), but the total will remain the same.
Simple Machines Allow for the same amount of workto be done, but with smaller forces Trade-off of using a smaller force isthat the force is applied through a longer distance Box lifted straight up a height h, force supplied is F = mg Force of gravity down inclined plane is F = mg sinq = mgh/LDistance pushed up plane = L
Power DE Power = = rate of energy usage Dt Can deliver the same amount of energy to a system using lesspower, but it takes a longer amount of time Our Western mindset usually screams for more powerEx. SUV’s require more powerful engines; larger homes require more powerful a.c. How much power do you expend by climbing 3 flights of stairs (10 m) in 10 seconds? If you have a mass of 70 kg and each flight is 5 m, then the power is P = (mgh)/dt = (70 kg)(9.8 m/s2)(15 m)/(10 s) = 1029 W