Rest of 8 the Chapter

Transcription

1 Rest of 8 the Chapter

2 Recall that we defined E (Mechanical) as the sum of KineDc and PotenDal energies ( all types taken into consideradon) mec E = K + U sys sys sys For an isolated system where there are only INTERNAL forces - ΔE mec = ΔK + ΔU = 0 sys sys sys

3 Recall that when conservadve forces act on system it results in increase in potendal energy Δ U = W c Conservative Forces ONLY

4 Work done by Ext Forces No FricDon involved W = ΔK + ΔU Comes from W- E theorem e.g. W spring W gravity = ΔK FricDon involved W = ΔK + ΔU + Δ(F f.d) W = ΔK + ΔU + ΔE thermal

5 ConservaDon of Energy in terms of Work Done Total energy E of a System can change only by amounts of energy that are transferred to and from the system. W = ΔK + ΔU + ΔE thermal + ΔE internal W = ΔE mechanical + ΔE thermal + ΔE internal

6 Isolated System An isolated system: is a system where there is no net work is done on the system by external forces. ΔE mec + ΔE th + ΔE int = 0 ΔE mec = E mec, Final - E mec, ini1al E mec, Final = E mec, ini1al - ΔE th - ΔE int

7 EXAMPLE In Fig., a 2.0 kg package of tamales slides along a floor with speed v1=4.0 m/s. It then runs into and compresses a spring, undl the package momentarily stops. Its path to the inidally relaxed spring is fricdonless, but as it compresses the spring, a kinedc fricdonal force from the floor, of magnitude 15 N, acts on it. The spring constant is N/m. By what distance d is the spring compressed when the package stops?

8 Forces 1)normal does no work 2) grav force - does no work 3) Spring force does work on the package decreasing its KE and increasing the PE 4) Spring force also pushes the rigid wall 5) Friction increases thermal energy Package+Spring+floor+wall -> isolated system as a whole E mec, Final = E mec, ini1al - ΔE th - ΔE int 0.5 Kd 2 = 0.5 mv 2 - f k d 5000 d 2 = d, d = m

9 Finding the ConservaAve Force AnalyAcally Solving for F(x) and passing to the differendal limit yield

10 Reading a PotenAal Energy Curve

11 Reading a PotenAal Energy Curve Turning Points: a place where K=0 (because U=E ) and the pardcle changes direcdon. Neutral equilibrium: the place where the pardcle has no kinedc energy and no force acts on it, and so it must be stadonary. unstable equilibrium: a point at which. If the pardcle is located exactly there, the force on it is also zero, and the pardcle remains stadonary. However, if it is displaced even slightly in either direcdon, a nonzero force pushes it farther in the same direcdon, and the pardcle condnues to move stable equilibrium: a point where a pardcle cannot move lec or right on its own because to do so would require a negadve kinedc energy

12 IdenAfy this system

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14 Pendulum modon is similar to a spring They both follow Simple Harmonic MoAon (SHM)

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16 A 2.00 kg pardcle moves along an x axis in one- dimensional modon while a conservadve force along that axis acts on it. The potendal energy U(x) associated with the force is ploeed in the Fig. That is, if the pardcle were placed at any posidon between x=0 and x=7m, it would have the ploeed value of U. At x=6.5m, the pardcle has velocity v 0 =(- 4.0m/s)i. (a) determine the pardcle s speed at x 1 =4.5m. (b) Where is the pardcle s turning point located? (c) Evaluate the force acdng on the pardcle when it is in the region 1.9m<x<4.0m. 16 point ; F = 4.3N

17 General Energy ConservaDon ext int mec W + WNC =Δ Ksys +Δ Usys =ΔEsys W int NC = ΔE NC W =ΔE W =Δ E +ΔE ext mec int mec NC sys NC sys For a isolated system where W ext is zero, its energy is conserved. mec NC Δ E +Δ E = 0 sys THE PRINCIPLE OF CONSERVATION OF ENERGY: Energy can neither be created nor destroyed, but can only be converted from one form to another.

18 In this figure, a block slides along a path that is without fricdon undl the block reaches the secdon of length L=0.75m, which begins at height h=2.0m on a ramp of angle θ=30 o. In that secdon, the coefficient of kinedc fricdon is The block passes through point A with a speed of 8.0 m/s. If the block can reach point B (where the fricdon ends), what is its speed there, and if it cannot, what is its greatest height above A? C

19 C

20 C