The figure below shows a plot of potential energy U versus position x of a 0.87

Question

The figure below shows a plot of potential energy U versus position x of a 0.87 kg particle that can travel only along an x axis. (Nonconservative forces are not involved.) Three values are UA = 25 J, UB = 45 J, and UC = 65 J. The particle is released at x = 4.5 m with an initial speed of 6.0 m/s, headed in the negative x direction. (a) If the particle can reach x = 1.0 m, what is its speed there, and if it cannot, what is its turning point? (b) What is the magnitude of the force on the particle as it begins to move to the left of x = 4.0 m? (c) What is the direction of the force on the particle as it begins to move to the left of x = 4.0 m? positive x direction negative x direction Suppose, instead, the particle is headed in the positive x direction when it is released at x = 4.5 m at speed 6.0 m/s. (d) If the particle can reach x = 7.0 m, what is its speed there, and if it cannot, what is its turning point? (e) What is the magnitude of the force on the particle as it begins to move to the right of x = 5.0 m? (f) What is the direction of the force on the particle as it begins to move to the right of x = 5.0 m? positive x direction negative x direction

Explanation / Answer

(a) Total energy of the particle = 12 + 6 = 18 J Kinetic energy of teh particle when it is at x = 3.5 = 18 - 9 = 9 J Let speed be v. We have 0.5*0.250*v^2 = 9 or v = sq rt[18/0.250] = 8.485 m/s (b) speed(at x = 6.5) = sq rt[{2*(18-0)}/0.250] = 12 m/s (c )turning point at right, say x = 'XR' will be where U(XR) = 18 J slope of U(x) from x =7 to 8 is (24-0)/21= 24 J/m . We have U(7) = 0 U(XR) = 18 and (18 - 0)/(XR - 7) = 24or XR-7 = (18/24) or XR = 7 + (18/24) = 7.75 m (d) turning point at left, say x = 'XL' will be where U(XL) = 18 J slope of U(x) from x =1 to 3 is (20-9)/2 = 5.5J/m . We have U!1) = 20 U(XL) = 18 and (20 -18)/(XL - 1) = 5.5 or XL -1 = (2/5.5) or XL = 1 + (2/5.5) = 7.5/5.5 = 1.364 m So the particle will move from 1.364 m to 7.75 m

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

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