=========================preview======================
(PHYS011)[2008](f)midterm~tliab^_10526.pdf
Back to PHYS011 Login to download
======================================================
Midterm examination PHYS011 (20 points for each problem)
Attentions:
(1) Detail steps should be given in your answers! Grades are given according to steps.

(2) Make clear drawings to express your thoughts when necessary.

(3) Hand writing should be clear and recognizable.




Problem 1
A single bead can slide with negligible friction on a wire that is bent into a circular loop of radius 10.0 cm, as in Figure. The circle is always in a vertical plane and rotates steadily about its vertical diameter. The position of the bead is described by the angle . that the radial line, from the center of the loop to the bead, makes with the vertical.
(a) With a period of 0.200 s, at what angle up from the bottom of the circle can the bead stay motionless relative to the turning circle? (5 points)
(b) Repeat the problem if the period of the circles rotation is 0.400 s. (5 points)
(c) Repeat problem (a) and (b) if there exists friction between the bead and the wire while the static friction coefficient is .s. (10 points)






Problem 2
Assume that as a particular object of mass m moves through a resistive medium, its speed decreases as described by the equation v=vi - kx, where k is a constant coefficient and x is the position of the object and vi is its speed at x=0.
(a) Find the expression of the resistive force. (5 points)

(b) Derive a mathematical expression of the speed as a function of time and plot it. (8 points)

(c) Calculate the work done by the resistive force between two points, xf and xi, and compare your result with its kinetic energy change. (7 points)



Problem 3
The potential energy of a diatomic molecule (molecule consisting of two
atoms) can be described by Lennard-Jones function, as shown by the U(x) curve.


Where x is the inter-atomic distance (separation between the two atoms)


(a) Calculate the force F between the two atoms. Qualitatively plot F as a function of x. (Please duplicate the U(x) curve in your answer paper and plot the F(x) curve below it using the same scale x axis). Describe how the magnitude and direction of the force change with the inter-atomic distance. Find the inter-atomic distance xMaxA at which the force is the largest attractive force. Mark xMaxA in the F(x) curve you plotted. (7 points)
(b) Find the equilibrium inter-atomic distance x0, mark x0 in the F(x) plot you drawn in (a). Calculate the minimum energy to break the molecule (separate the two atoms infinite far away). (3 points)
(c) An external force increases the inter-atomic distance from x0 to 2x0, calculate the work done by the external force. Shade the area representing this work in the F(x) plot you drawn in (a). (3 points)
(d) If the external force is removed at inter-atomic distance of 2x0, describe the motion of the atoms and energy conversion of the system. Calculate the total kinetic energy of the system when the inter-atomic distance is 1.5x0. Write an expr