Classical Mechanics Homework Assignment #11, due by 5 pm Monday November 7 to Krishna’s office Lab 2 3255. All problems from Taylor except as indicated.

1. Choose one of 7.20, 7.22, or 7.23 that you didn’t do for Homework #10
2. Choose one of 7.29, 7.30, or 7.35 that you didn’t do for Homework #10
3. 7.50
4. 7.52 (see note)
5. Consider a simple pendulum with mass m and (massless) string of length b, released from rest at an angle θ₀ with respect to vertical. Determine the tension in the string as a function of angle θ and other given and known constants. Check that your answer makes sense in the limit cases when θ = θ₀ (i.e. at the top of the swing) and when θ = 0 (the bottom of the swing). This is the problem we discussed in class; recall from that discussion that we could only get so for with the Lagrangian method, so don’t hesitate to use a Newtonian framework as needed. (see note)
6. There are only five problems on this homework set.

Notes:

• For 7.52, convince yourself that the geometry requires x = RΦ, so that the constraint is f(x, Φ) = x – RΦ = 0.
• For Problem 5, here’s a necessary intermediate step you can use to check your work: v² = 2gb(cos θ – cos θ₀)