物理习题（英文版）Introductory Physics I
2012
Homework assignment 5
Please hand in on Monday, 26.10.2012 in class. ! Please write clearly !
Problem 1. A solid sphere (radius = R) rolls without slipping in a cylindrical trough (radius = 5R). Show that, for small displacements...
Introductory Physics I
2012
Homework assignment 5
Please hand in on Monday, 26.10.2012 in class. ! Please write clearly !
Problem 1. A solid sphere (radius = R) rolls without slipping in a cylindrical trough (radius = 5R). Show that, for small displacements from equilibrium perpendicular to the length of the trough, the sphere executes simple harmonic motion. Calculate the period T in terms of R and g.
Problem 2. A pendulum of length L and mass M has a spring of force constant k connected to it at a distance h below its point of suspension. Find the frequency of vibration of the system for small values of the amplitude (small Θ). Assume the vertical suspension of length L is rigid, but ignore its mass.
Problem 3. Two blocks that have masses m1 and m2 are attached to either end of a spring that has a force constant k and are set into oscillation by releasing them from rest with the spring stretched.
a) Calculate the oscillation frequency ω.
b) In one of your chemistry labs, you determine that one of the vibrational modes of the HCl molecule has a frequency of ω = 8.969 x 1013 Hz. Find the “effective spring constant” between the H atom and the Cl atom in the HCl molecule.
It is advantageous to use the definition of ‘reduced mass’ µ in this problem:
Problem 4. (Hard problem – work in a team if you have difficulties) There is an old pendulum clock in your grandmother’s house. The uniform rod of length L = 2 m has a mass m = 0.8 kg. Attached to the rod is a uniform disk of mass M = 1.2 kg and radius 0.15 m. The clock is constructed to keep perfect time if the period of the pendulum is exactly 3.50 s.
(a) What should the distance d be so that the period of this pendulum is 2.50 s?
(b) Suppose that the pendulum clock loses 5 min/day. To make sure your grandmother will not be late for her quilting parties, you decide to adjust the clock back to its proper period. How far and in what direction should you move the disk to ensure that the clock will keep perfect time?
(please always derive the full equations d = f(L,M,m,T) BEFORE entering the specific values (2m, 0.8 kg, etc.)
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