# אנרגיה פוטנציאלית ושימור האנרגיה

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• . 10 " , . " ?

• . . ( ). : " . . .

• 2. . . . K = W . . .

• . " , . U U = -W

• . , , . , . . , .

• :1. .2. .3. , W1 , K . 4. , W2 .Conservative and Nonconservative Forces

• W1 = W2, , . . . . , . , . .

• I: . II: . ? a - b , .

• ab12Wab,1 =Wab,2Wab,1 + Wba,2 = 0Wab,1 = Wba,2Wab,2 = Wba,2 F . W. xfW = F(x) dx = U xi

• : yf yfU = ( mg)dy = mg dy = mg (yf yi) yi yiU = mg yU Ui = mg (y yi) Ui yi. . Ui = 0 yi = 0 . y y=yi. .

• : xf xf U = ( kx)dx = k x dx xi xiU = ()kxf2 ()kxi2 xi = 0. U = ()kx2 k. xi xf F = -kx .

• - x x = 0 - x = xf , x, . . F1. . xfxfxfF1F1F1xfU = F(x) dxxiiiiiii

• i. xfU = [F1 (F1/xf) x] dx = [F1xf ()(F1/xf) xf2] 0U = ( ) F1xfii. xfU = F1 dx = F1xf 0iii. xfU = [ F1 + (F1/xf) x] dx = [ F1xf + ()(F1/xf) xf2] 0U = () F1xf

• .Emec = K + U . . W , K U . : K = W : U = W : K + U=0 .

• K + U = 0 K2 K1 = ( U2 U1)K2 + U2 = K1 + U1 Emec,2 = Emec,1 , . II .

• . . .

• 4 . . . B .

• bungee 61 " 45 L 25 . 160 N/m. . h . - d. .K + Ue + Ug = 0

• Ug = mg y = mg ( L +d )Ue = ()kd2K = 00 + ()kd2 mg ( L +d ) = 0()d2 mgd/k mgL/k =0 d = (mg/k) (m2g2/k2 +2mgL/k)d = 17.9 m = 42.9 m 25 + 17.9 , 2.1 .

• . . x. .U(x)

• 1. U = W = F(x) xF(x) = U/x F(x) = dU/dx U(x) = kx2 U(x) = mgx F(x) = kx F(x) = mg

• 2. U(x). F(x) ( ) .

• x2. U(x) , . . . x3 . .

• 3. U(x) + K(x) = EmecK(x) = Emec U(x) Emec = 5J . . x1. , , . ( ) . .

• 4. x < x0x = x2 x = x3x = x4x >x5 , . x x5 . . x2 x4 . U(x). dU/dx .

• " . " . . " (K=W) . , . (- ), . .

• : , . . .W = K + UW = EmecEmec = K + U

• v0Ffkdv F d, - v0 -.v fk. F fk = mav2 = v02 + 2ad a = (F fk) / m v2 = v02 + 2 d (F fk) / m Fd = mv2 mv02 + fkdFd = K + fkd , .Fd = Emec + fkd

• . . . , . .Eth = fkdFd = Emec + Eth W = Emec + Eth .WEmecEth

• "" . 25 9000 " 45 2 . F ? 80 ".F = 252mg W = 50mgd cos0 = 50809.8451 = 1.8 106J = 1.8 MJ

• W = Eth + Emec . (K = 0) (U = 0). : . 10 " ?W = 50mgd cos0 = 50809.81041 = 3.9108 J 400 MJ . .

• .W = E = Emec + Eth + Eint . . . , , .

• . Emec + Eth + Ein = 0 1 2.Emec,2 = Emec,1 + Eth + Ein . Emec,1 + Eth,1+Eint,1 = Emec,2 + Eth2+Eint,2 Emec,2 = Emec,1

• .Pavg = E / tP = dE / dt -:1 kW hour = 1000 watt 3600 s = 3.6x106 J 360 !Work = 1000 10 360 = 3.6x106 J[P] = J/s = watt = W

• 6 " 7.8 / 8.5 . 11.1 . . . Emec + Eth = 0 K = 0 ()mv02U = mgy mgy0Eth = EmecEth = ()mv02 mg(y y0) = 30 J

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