Problem: Spring pulls on mass. Again use Wnet=Ws W/=AKE W=-umg d kd △K=-mv kd-umg d=my △r △AAA∧园 stretched position(at rest m umg relaxed position Physics 121: Lecture 13, Pg 16
Physics 121: Lecture 13, Pg 16 Problem: Spring pulls on mass. Again use Wnet = WS + Wf = KE Wf = - mg d stretched position (at rest) d relaxed position vr m m i f = mg r WS = kd 1 2 2 2 mvr 2 1 K = 2 r 2 mv 2 1 kd mgd 2 1 − =
Conservative forces In general, if the work done does not depend on the path taken, the force involved is said to be conservative Gravity is a conservative force W=GMm R2 R1 Gravity near the Earth's surface Wa=-mgAy A spring produces a conservative force Physics 121: Lecture 13, Pg 17
Physics 121: Lecture 13, Pg 17 Conservative Forces: In general, if the work done does not depend on the path taken, the force involved is said to be conservative. Gravity is a conservative force: Gravity near the Earth’s surface: A spring produces a conservative force: Wg = −mgy = − 2 1 g R 1 R 1 W GMm
Conservative Forces: We have seen that the work done by a conservative force does not depend on the path taken W=W Therefore the work done in a closed path is 0 W WNET=W,-W2=0 The work done can be reclaimed Physics 121: Lecture 13, Pg 18
Physics 121: Lecture 13, Pg 18 Conservative Forces: We have seen that the work done by a conservative force does not depend on the path taken. W1 The work done can be “reclaimed”. W2 W1 W2 W1 = W2 WNET = W1 - W2 = 0 Therefore the work done in a closed path is 0
Potential Energy For any conservative force F we can define a potential energy function U in the following way W=-△U The work done by a conservative force is equal and opposite to the change in the potential energy function This can be written as r29U2 △U=U2-U1=-W Physics 121: Lecture 13, Pg 19
Physics 121: Lecture 13, Pg 19 Potential Energy For any conservative force F we can define a potential energy function U in the following way: The work done by a conservative force is equal and opposite to the change in the potential energy function. This can be written as: W = - U U = U2 - U1 = - W r1 r2 U2 U1