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

Question

A 20 kg object is acted on by a conservative force given by F = -3.0 x - 5.0 x^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. What is the potential energy of the system associated with the force when the object is at x = 3.0 m? J If the object has a velocity of 5.0 m/s in the negative direction of the x axis when it is at x = 8.0 m, what is its speed when it passes through the origin? m/s 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? J m/s

Explanation / Answer

potential energy U(x) = - F dx = 3x2 /2+ 5x3/3 + U(0)

a) if U(0) = 0, U(3.0) =1.5x2 + 5x3/3 = 58.5 J

b) at x = 8.0 m, energy E = mv2/2 + U(8.0) = 1199.3 J

at x = 0, energy = mv'2/2 + U(0) = E = 250 J,

v' = (2E/m) = [v2+ 2U(8.0)/m] = 9.8 m/s

c) if U(0) = -8J,

U(x) =1.5x2 + 5x3/3 - 8.0

U(3.0) = 50.8 J

v' is unchanged, v' = 9.8 m/s

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.