A 20 kg object is acted on by a conservative force given by F = -3x - 5.x2, with

Question

A 20 kg object is acted on by a conservative force given by F = -3x - 5.x2, 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 = 6.0 m? (b) If the object has a velocity of 3 m/s in the negative direction of the x axis when it is at x = 8 m, what is its speed when it passes through the origin? What are the answers to (c) (a) and (d) (b) if the potential energy of the system is taken to be -6 J when the object is at x = 0?

(a)

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(b)

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(c)

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(d)

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Explanation / Answer

Here is what I solved before, please modify the figures as per your question. Please let me know if you have further questions. If this helps then kindly rate 5-stars

A 20 kg object is acted on by a conservative force given by F =-3.0x - 5x2, with F in Newtons and x in meters. Take thepotential energy associated with the force to be zero when theobject is at x = 0.
a. What is the potential energy of the system associated with theforce when the object is at x =2.0 m?
b. If the object has a velocity of 4.0 m/s in the negativedirection of the x axis when it is at x = 5.0 m, what is its speedwhen it passes through the origin?
c. What are the answers to (a) and (b) if the potential energy ofthe system is taken to be -8.0 J when the object is at x = 0?

sol:

potential energy U(x) = - ? F dx = 1.5x2 + 5x3/3 + U(0)
a) if U(0) = 0, U(2.0) = 1.5x2 + 5x3/3 = 19.3 J
b) at x = 5.0 m, energy E = mv2/2 + U(5.0) = 405.8 J
at x = 0, energy = mv'2/2 + U(0) = E = 405.8 J,
v' = ?(2E/m) = ?[v2 + 2U(5.0)/m] =6.37 m/s
c) if U(0) = -8.0 J,
U(x) = 1.5x2 + 5x3/3 - 8.0
U(2.0) = 11.3 J
v' is unchanged, v' = 6.37 m/s

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