ENERGY The ability to do work

ENERGY COMES IN MANY FORMS A. MECHANICAL

B. ELECTRICAL

C. CHEMICAL

WORK: A force acting through a distance, in the direction of the force. Units; Joules, Nm, Btu, cal, ft-lb Formulas: a.W=Fxd b.W=Fxdxcos  c.W=Fxrx  d.W=Tx 

Work is defined graphically by the area under the curve in a graph that shows force as the independent variable and distance as the dependent variable Variable Constant

A force can be exerted on an object and yet do no work.

W = F x d x cos  a.F is the force b.d is the displacement c.Theta is the angle between the force and the displacement vector. and is associated with the amount of force which causes the displacement

When determining the measure of the angle in the work equation, it is important to recognize that the angle has a precise definition - it is the angle between the force and the displacement vector. If the force is applied parallel to the incline, the displacement of the cart is also parallel to the incline. Since F and d are in the same direction, the angle is 0 degrees

a.As long as the work done is parallel to the plane that the object traverses, the cos  will be 0 0. b. If the plane that the object moves on is at an angle and is frictionless, then F net is not (F w sin  ’-  F w cos  ’) but will be F w sin  ’,there is nothing to resist the applied force. c. As the plane increases the applied force increases d. Because the plane reaches to a specific height, as the angle of the plane increases the length of the plane decreases. e. Therefore, work remains the same for any mass that is taken to a specific height along the surface of a frictionless plane

Apply the work equation to determine the amount of work done by the applied force in each of the three situations described below.

The quantity work has to do with a force causing a displacement. Work has nothing to do with the amount of time that this force acts to cause the displacement. Sometimes, the work is done very quickly and other times the work is done rather slowlywork The quantity which has to do with the rate at which a certain amount of work is done is known as the power POWER

The standard metric unit of power is the Watt A Watt is equivalent to a Joule/second One horsepower is equivalent to approximately 746 Watts

To be a powerful lineman you should be strong (apply a large force) and quick (displacement occurs over a short period of time).

A Walker -work done is large -time is very large -power rating would be small A Rock Climber -work done is large - it takes less time than the walker - power rating would larger than the walker A Bicycler - work done is large - it takes less time than the walker and rock climber - power rating is larger than the rock climber

A student does 82 J of work when lifting her textbooks from the floor to her desk. It took her 3.0 s to do this task. What is her power? Solution:

Since work done is approximately equal to the energy used, W = ~E, power can also be described as the rate at which energy is used.

To determine power produced by a moving object you must know its force and average velocity. Where,

A 1.0 x 10 3 kg car accelerates from rest to a velocity of 15.0 m/s in 4.00s. Calculate the power ouput of the car in 4.00s. Check Your Understanding

All machines are typically described by a power rating. The power rating indicates the rate at which that machine can do work upon other objects. Thus, the power of a machine is the work/time ratio for that particular machine

Law of Conservation of Mechanical Energy: -The sum of the potential and kinetic energy of an ideal energy system remains constant.

Gravitaional and Elastic forces are “conservative forces” because they are responsible for the exchange between Potential and kinetic energy in simple harmonic motion Conservative Forces

Dissipative Forces a.There are forces that produce deviations from the law of conservation of mechanical energy. b. Friction is an example of such a force. c. These forces are called “nonconservative” or “dissipative.” d. Friction is a dissipative force because it produces a form of energy (heat) that is not mechanical. e. Energy is lost f. In view of the law of the conservation of energy there is truly no loss in energy. g. Another observation to distinguish between conservative and dissipative forces is to note the relationship between the force and the path over which it acts.

Potential Energy Potential energy exists whenever an object which has mass has a position within a force field. The most everyday example of this is the position of objects in the earth's gravitational field. The potential energy of an object in this case is given by the relation: PE = mgh

Hydroelectric power is generated this way. As the water falls, it turns a turbine, which pushes electrons around creating an electric current. Gravitational Potential Energy Application

Elastic Potential Energy Anything that can act like a spring or a rubber band can have elastic potential energy. A rubber band stores energy when stretched and releases it as kinetic energy

Springs work the same way, but you can either stretch or compress them. Wind-up watches store potential energy in an internal spring when you wind them and slowly use this energy to power the watch.

Chemical Potential Energy The amount of energy in a bond is somewhat counterintuitive - the stronger or more stable the bond, the less potential energy there is between the bonded atoms. Strong bonds have low potential energy and weak bonds have high potential energy.

Lot's of heat and/or light energy is released when very strong bonds form, because much of the potential energy is converted to heat and/or light energy. The reverse is true for breaking chemical bonds. It takes more energy to break a strong bond than a weak bond. The breaking of a bond requires the absorption of heat and/or light energy.

PE = Energy (in Joules) m = mass (in kilograms) g = gravitational acceleration of the earth (9.8 m/sec2) h = height above earth's surface (in meters)

KINETIC ENERGY: -An object in motion has the ability to do work and thus can be said to have energy. -From the Greek kinetikos, meaning “motion” a.In order to obtain a quantitative definition for kinetic energy, we have to consider a particle mass “m” that is moving in a straight line with an initial speed v 1 b. To accelerate it uniformly to a speed v 2, a constant net force F is exerted on it parallel to its motion over distance d. c. Then the work done on the particle is W=Fd d. Apply Newton’s second law, F=ma e. Subsitute v 2 2 = v ad for a f. Then we find W=Fd=mad=m(v 2 2 -v 2 1 /2d)d or W=(.5)mv 2 2 -(.5)mv 2 1 g. We define the quantity (.5)mv 2 to be the translational kinetic energy KE=(.5)mv 2

WORK ENERGY THEOREM: The work done on a particle by the net force acting on it is equal to the change in kinetic energy of the particle. W =  KE = 1/2mv 2 2 – 1/2mv 2 1 a.The left-hand term represents the net work done on the particle. b. The right hand side of the equation is the difference between the final and initial kinetic energies. c. If the work done on the particle is positive, then its kinetic energy increases. d. The theorem emphasizes that work, or equivalently energy, is needed to set a particle in motion. e. The theorem is valid for constant and variable forces.

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