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Exam I

Exam I. Power. We are often concerned with not only how much energy it takes to do something (say get a car up to a certain kinetic energy) but also how quickly that energy can be transferred. POWER : the rate at which energy is transferred. P = dW/dt P avg = W /D t.

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Exam I

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  1. Exam I

  2. Power We are often concerned with not only how much energy it takes to do something (say get a car up to a certain kinetic energy) but also how quickly that energy can be transferred. POWER : the rate at which energy is transferred. P = dW/dt Pavg = W/Dt

  3. The Rolls-Royce "Trent 800" series of jet engines have a thrust rating of up to 420 kNewtons. Two of these engines power some versions of the Boeing 777 aircraft. If such an aircraft is traveling at 240m/s (854 km/hr) with both of its engines operating at full capacity, what is the power being generated by each engine? What happens to all this energy?( 16 correct; 12 incorrect (mainly silly mistakes, units etc.); 29 no answ.) W=F*d =› W=854km/hr*420000N=358680000J. P=W/t =› 358680000J/1sec=358680000watts. Due to conservation of energy, all this energy does not disappear. The aircraft expends 1.008 x 10^8 watts of energy. Most of the energy is transformed into heat, motion, sound and other forms of energy. Two questions: Does gravity do any work in this situation? What does the work done by drag do???

  4. Variable Forces IF the force is not constant, we have to look at: dW = Fx(x) dx (increment of work performed is the product of the x Force component and the incremental displacement) We have seen that springs provide forces whose magnitude increases as the spring is compressed or expanded more F = - k (x-xo) ; k is the spring constant (what is the significance of the -?) W = -½ k (x-xo)2

  5. What is the property that a force must possess if it is possible to define a potential energy associated with that force? (6 said “conservative” but only a few people explained what that means; 22 were off the mark 26 no answers) • There were a large number of seemingly random suggestions. I guess people have not yet looked at chapter 8 (my mistake).

  6. Chapter 7 problems

  7. In class, I will use the expression U = 1/2k (x-x_o)^2 for the potential energy of a spring. Comment briefly on the difference between this and U = 1/2kx^2, which is the form given in most texts. What is the significance of the term xo? Which form would you find more useful? (24 “initial position” 7 “equilibrium position” 1 Other 23 no reply) • I don’t know if this reflects confusion, or just careless wording of responses, but be careful. Simlar symbols can, unfortunately, mean different things in different contexts!!

  8. Chapter 8: Potential Energy • A conservative force is one for which the work done around ANY closed circuit • is ZERO • A VERY important consequence of this is that: • The work done by a conservative force in going from a to b depends ONLY • on the two points a and b, NOT on the path taken between them!!! • Note: this allows us to define a CHANGE IN ENERGY associated with the • CHANGE IN POSITION (from a to b).

  9. Chapter 8: Potential Energy Check point 1 is the force acting here conservative?

  10. Chapter 8: Potential Energy Check point 1 is the force acting here conservative? NO!!!

  11. Chapter 8: Potential Energy Check point 1 is the force acting here conservative? NO!!! But it could be conservative if the bottom path was -60 J rather than + 60J. -

  12. Chapter 7 examples

  13. Chapter 8 Examples g. How fast would the car be moving at point C?

  14. Potential Energy Curves and Conservative Forces F(x) = - dU/dx

  15. Chapter 8 Problems (cont.)

  16. A parachutist is drifting downward at a constant speed of roughly 1m/s after his chute has opened. If the combined mass of the parachutist and his equipment is 85.0 kg, at what rate is he losing gravitational potential energy? Where is this lost potential energy going? • (833 W: 17, but 5 had units wrong; others 8 no answer 28) • He is losing gravitational energy at a rate 1666.67 J/s. This lost potential energy is going into kinetic energy. (I have no idea where this number came from? Think: the PE is decreasing, but is the KE increasing??) • He is losing gravitational potential energy at a rate of -833.85 Newtons per second The potential energy is converted into the kinetic energy of him falling. (watch your units) • Energy of potential energy due to gravity: E=mgy= 85x9.8(1) 833 j/s The energy is being transferred by way of the dissipative drag force to thermal energy which is distributed throughout the environment. (very good)

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