lecture7

# lecture7 - Phys 2101 Gabriela González • There is...

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Unformatted text preview: Phys 2101 Gabriela González • There is potential energy associated with the work of conservative forces (gravity: U=mgh; springs: U= ½ kx 2 ): Δ U = U f – U i = ¡ W • If the only forces doing work are conservative the sum of kinetic and potential energy is conserved: Δ U + Δ K = 0 U f + K f = U i + K • If there are non-conservative forces, the change in the total energy (potential + kinetic) is equal to the work done by those forces: Δ U + Δ K = W other 2 3 U(h)=mgh h x U(x) = ½ kx 2 Where is F=0? (equilibrium position) 4 Δ U = − W = − F ( x ) dx ∫ ⇒ F ( x ) = − dU ( x ) dx • Force = slope of U(x) curve • Equilibrium: F=0 = dU/dx. d 2 U/dx 2 >0: stable eq; • If E=KE+U, when U(x)=E, KE =0 and v=0: turning point • If E=KE+U, since KE is +ve, U<E: only certain positions are allowed. 4 Δ U = − W = − F ( x ) dx ∫ ⇒ F ( x ) = − dU ( x ) dx • Force = slope of U(x) curve • Equilibrium: F=0 = dU/dx. d 2 U/dx 2 >0: stable eq; • If E=KE+U, when U(x)=E, KE =0 and v=0: turning point • If E=KE+U, since KE is +ve, U<E: only certain positions are allowed. 5 Figure 8-48 shows a plot of potential energy U versus position x of a 0.90 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) The particle is released at x = 4.5 m with an initial speed of 7.0 m/s, headed in the negative x direction. (a)If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? What are the (b) magnitude and (c) direction of the force on the particle as it begins to move to the left of x = 4.0 m? Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 7.0 m/s. (d) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? What are the (e) magnitude and (f) direction of the force on the particle as it begins to move to the right of x = 5.0 m?...
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## This note was uploaded on 12/01/2011 for the course PHYS 2101 taught by Professor Grouptest during the Fall '07 term at LSU.

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lecture7 - Phys 2101 Gabriela González • There is...

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