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Energy Review Brandon Demory Ch 7 and Ch 8 (p408-433) Ch14(all) Overview Energy- the ability to do work Types of energy: 1. Kinetic: The energy associated with motion. K=½mv2 2. Potential: The energy associated with position. Two particular types are gravitational potential energy and elastic potential energy. U= mg (yf - yi) and U= ½kx2. ∆U= -∫ F(x)dx. Work Work: energy transferred to or from an object via a force acting on the object. It is also the integral of a variable force. W= Fd or Fd cos(θ) or F→ dot d→. Work- Kinetic Energy Theorem The change in Kinetic Energy of an object is equal to the net work of an object. ∆K= W= Kf –Ki= Wapplied + Wgrav Work done by a gravitational force is defined as: W= mgd cos(θ). F=ma; v2= vo2 +2ad; ½mv2 - ½mvo2= Fd The net work on an object is equal to the sum of the works done by the forces. Work cont. Work done by a spring force: W= ½kxi2 - ½kxf2. For a variable force, we take the integral of the force over the distance interval. W= ∫F∆x or ∫F dx For work in more than one dimension, the sum of the work components equals the total work. W= ∫Fx dx + ∫Fy dy + ∫Fz dz. Power - The time rate at which work is done by a force. Pavg= W/∆t; Pavg= ∆E/∆t -Instantaneous power is the instantaneous time rate of doing work. P= dW/dt. Power is also the Force dot the velocity. (instantaneous power) P= Fd; P= dW/dt= F cos(θ) dx/dt= Fv cos(θ) P= dE/dt Mechanical Energy -The sum of the Potential and Kinetic Energy of a system. Emec = K + U -For an isolated system, the mechanical energy of the system is conserved. U1 + K1 = U2 + K2. -From this we can see that: ∆Emec= 0 = ∆K + ∆U W= ∆Emec. This is work done on a system by an external force. (friction involved) W= ∆Emec + ∆Eth; ∆Eth= f*d (frictional force; sliding) Conservation of Energy - The total energy of a system can change only by amounts of energy that are transferred to or from the system. - In an isolated system, the total energy cannot change. Therefore: ∆Emec + ∆Eint= 0 Conservative force • The work done by a conservative force on a particle moving between two points does not depend on the path taken by the particle. • So, for a round trip, the net work done by the conservative force is zero. Wab,1 + Wba,2 = 0; Wab,1 = -Wba,2 For path ab2, the work done by the force to go from a to b is the opposite of the work to go from b to a. therefore, Wab2 = -Wba,2 Using substitution of Wab2 for –Wba,2, we find: Wab,1 = Wab2 How do you find the work done by a variable force? You must take the integral of the force. W= ∫F∆x In an isolated system, the change in energy always adds up to _____. zero The kinetic energy of a system is always _______ or zero and never ______. Positive, negative The Work- Kinetic Energy theorem states that: ∆K= Wnet= Kf –Ki The sum of the Kinetic energy and potential energy of a system is the ________. The Mechanical energy Power is _____. The time rate at which work is done For an object falling at a constant velocity, which of the following does not change for the system. A) Total energy B) kinetic energy C) Wavelength D) potential energy B) Kinetic energy The formula for spring potential energy is: U=½kx2 The net work done on an object is______: The sum of the individual works An object of mass 1 kg moving at 2 m/s has a kinetic energy of ____. 2 Joules The units for all forms of energy are ____. Joules The formula for work is: Fd cos() All of the following are ways to describe power except: a) W/∆t b) dE/dt c) Fv cos(θ) d) Fd cos(θ) D) Is correct Two ways to describe a conservative force_____. One in which the net work the force does on the particle moving around any closed path from a starting point back to that point is zero. Or a path independent force. Gravitational Potential Energy is defined as: U= mgh Energy is conserved in a system if: There is no external force acting on the system. A 2.0 kg mass hanging 3 meters from the ground has a gravitational potential energy of; g= 10 m/s2 U= 60 Joules Friction is a conservative or nonconservative force? Non-conservative force What is the velocity of a 3 kg object that has a kinetic energy of 24 Joules? 4 m/s True of False: Worknet = -U (potential energy) True A mass of 1 kg has a Kinetic energy of 8 Joules. 28 joules of work are applied to the mass. Find its new velocity. W=Kf-Ki; 28=K-8; K=36=.5*1*v2. V=√72 m/s A mass of 1 kg is attached to an oscillating spring with a spring constant of 4N/m. At equilibrium, the spring has 18J of Kinetic energy. Find the maximum amplitude of its oscillation if there are no external forces in the system. X= 3 meters A helicopter lifts a 36 kg mass 4 meters vertically from the ocean. How much work is done by the gravitational force? -1.4Kj Power is measured in______. Watts An object with an instantaneous velocity of 3 m/s that has a constant force of 2N applied to itself has an instantaneous power of: 6 Watts An object (mass 2 kg) has an initial velocity of 3 m/s. The frictional force on the object is a constant 1N. a) How far will the object slide before it stops? b) If it took 3 seconds for the box to stop moving, what was the average power? a) D=9 meters b) Pavg=3 watts If a person lifts on object to a higher height, is the work done by gravity positive or negative work? Negative Work True or False Instantaneous Power is defined as P= ∆E/∆t False; it is actually dE/dt For an isolated system, if an object starts with 20 Joules of K energy and 10 Joules of U, and at another instant, has 16 joules of U, what is the Kenergy of the object? 14 Joules For a force defined by the function F=3x; the work done in the system as the object moves from x=1 to x=3 is? W=∫Fdx= ∫3x dx=(3/2)x2; W=(3/2)(32-12)=12 joules