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16 should be correct since 17 has friction doing positive work

right I mixed up Pe and Ke so is the equation in post #16 correct? I think my equation in post #17 is the correct solution

or is this equation wrong should it be PE = KE - W(friction) so KE = PE + W(friction) 1/2mv^2 = 1/2k(x1^2 - x2^2) + (uk)(m)(g)(x) and solving for v, v = 2.036 m/s

aren't those the equations we just solved for I don't know what else it would be Ke = Pe - W (friction) Ke = Pe - F (friction)(x) 1/2mv^2 = 1/2k(x1^2 - x2^2) - (uk)(m)(g)(x)

So PE (total) = Ke - W (friction) = 1/2k(x1^2 - x2^2) - (uk)mgx

ok so once we have obtained the Potential energy using Pe = 1/2k(x1^2 - x2^2) = 1.49792 Nm do we just set that equal to 1/2mv^2 so, v^2 = {k(x1^2 - x2^2)}/m sqrt[(42 N/m){(0.28m^2)-(-0.084m^2)}/1.2]= 1.58 m/s

Remaining... So X would actually be 0.195914286 from 0.280 - 0.084 m Where W (spring) = 1/2kx^2 = 0.806 Nm W (friction) = Fx = 0.692 NM W tot = W (friction) - W (spring) W tot = 0.114 NM W tot = 1/2 mv^2 V = 0.43

W (spring) = 1/2kx^2 = 0.14847855 Nm W (friction) = Fx = 0.296957109 NM W tot = W (friction) - W (spring) W tot = 0.148478559 NM W tot = 1/2 mv^2 V = 0.4974578022 This seems wrong the velocity of the box at equilibrium is greater

-kx = uk m g -X = [(0.3)(1.2 kg)(9.81 m/s2)]/42 X = -0.0840857143 Compressed by 0.084 m from equilibrium

F net= 0 F (friction) = F (spring)

when acceleration = 0

Max speed occurs when all energy has been translated from spring into box. E (Potential) = 1/2kx^2 E (Potential) = (1/2)(42 N/m)(0.280 m)^2 = 1.6464 N m Ep = Ek =1/2mv^2 1.6464 N m= 1/2 (1.2 kg) v^2 v = 1.6565 m/s

what would the equation be for that the 0 friction is throwing me off. would it just be 6 m/s2 from 12N = 2kg a??

there is the gravitational force, the applied force, and the frictional force the applied force is applied by the bottom block