A 20 kg object is acted on by a conservative force given by F = -3.0x-5.0x^2, wi

Question

A 20 kg object is acted on by a conservative force given by F = -3.0x-5.0x^2, with F in newtons and x in meters. Take the potential energy associated with the force to be zero when the object is at x = 0. (a) What is the potential energy of the system associated with the force when the object is at x = 2.0 m? (b) If the object has a velocity of 4.0 m/s in the negative direction of the x axis when it is at x = 5.0 m, what is its speed when it passes through the origin? (c) What are the answers to (a) and (b) if the potential energy of the system is taken to be -8.0 J when the object is at x = 0? *** Please show steps on how to solve the questions to get a 5 star rating. Thanks.

Explanation / Answer

potential energy(P.E) = F.x => P.E = (-3.0x - 5.0x^2).x => P.E = -3.0x^2 - 5.0x^3 a)P.E at x = 2.0m is -3.0(2)^2 - 5.0(2)^3 = -12 - 40 = -52J b) energy conservation. K.E1 + P.E1 = K.E2 + P.E2 .5(20)(4)(4) +(3(25)+5(125)) = .5(20)(v^2) + 0 (displacement is in -ve direction) 160 + 700 = 10v^2 => v^2 = 86 => v = 9.27m/s if P.E at origin is -8J then a) -52J +(-8)J = -60J b) 160 + 700 = 10v^2 -8 => v^2 = 85.2 => v = 9.23m/s

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