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  2. ENERGY is present in the Universe in a variety of forms, including mechanical, chemical, electromagnetic, and nuclear energy. • Mechanical energy, is a sum of Kinetic energy (the energy associated with motion), and potential energy (the energy associated with position)

  3. WORK-is done only if an object is moved through some displacement while a force is applied to it • The WORK done on an object by a constant force F is give by: W = FΔx F- the magnitude of the force Δx- magnitude of the displacement • SI unit: joule (J)= newton meter = N m = kg m2/s2

  4. Work is a scalar quantity • The work done by a constant force F is given by: W= (F cosθ)Δx F-is the magnitude force Δx – the magnitude of the object’s displacement θ- the angle between the directions F and Δx • Work can be either positive or negative, depending on whether cos θ is positive or negative

  5. Wnet= FnetΔx =(m a) Δx v2 =vo2 +2a Δx aΔx = (v2-vo2)/2 W= m (v2-vo2)/2 W= ½ mv2-½ mvo2 The KINETIC ENERGY of an object of mass m moving with a speed v is defined by: KE=1/2 mv2 SI unit: (J)=kg m2/s2 • The net work done on an object: Wnet= Kef –Kei =ΔKE where the change in the kinetic energy is due entirely to the object’s change in speed

  6. A force is conservative if the work it does moving an object between two points is the same no matter what path is taken (ex gravity) Nonconservative forces don’t have this propriety (ex friction force)

  7. The Work – Energy theorem: Wnet= Kef –Kei =ΔKE Can be written in terms of the work done by conservative forces (Wc) and the work done by nonconservative forces (Wnc) Wnet= Wnc +Wc =ΔKE The work done by conservative forces is called POTENTIAL ENERGY – a quantity that depends obly in the beginning and end points of a curve, not the path taken

  8. Gravity is a conservative force, then a potential energy can be found. • If a book falls from height yi to a height yf, we neglect the force of air friction, so the only force acting is gravitation • How much work is done? Wg= F Δy cosθ = mg (yi-yf) cos0o = -mg (yf-yi)

  9. Wnet = Wnc +Wg =ΔKE Wnet = Wnc –mg (yf-yi) =ΔKE Wnc =ΔKE +mg (yf-yi) The gravitational potential energy of a system consisting of the Earth and an object of mass m near the Earth’s surface is give by: PE= mgy SI unit : (J)- joule g- acceleration of gravity y – vertical position of the mass relative the surface of Earth

  10. Wg = - (PEf-Pei) = - (mgyf-mgyi) Wnc = (KEf- KEi) + (PEf –PFi) The work done by nonconservative forces, Wnc is equal to the change in the energy plus the change in the gravitational potential energy !!! It is important to choose a location at which to set that energy equal to zero (y=0)

  11. Gravity and the Conservation of Mechanical Energy When a physical quantity is conserved the numeric value of the quantity remains the same throughout physical process (final value is the same as its initial value) KEi + PEi = KEf +PEf The sum of kinetic energy and the gravitational potential energy remains constant at all the times , is a conserved quantity

  12. Total mechanical energy : E = KE +PE The total mechanical energy is conserved! In any isolated system of objects interacting only through conservatives forces, the total mechanical energy E= KE +PE, of the system, remains the same all times