1. (3) Marion & Thornton: problem 1-29.

Hint: use the gradient function to find vectors perpendicular to each of the two surfaces at the specified point. Then use the scalar product to find the angle between those two vectors.

2. (3) Marion & Thornton, problem 2-26.

Hint: Use the concepts of work and energy, rather than F=ma, to solve this problem.

3. (3) Marion & Thornton, problem 2-29.

An "8% grade" means that the slope = 8% = 0.08.

4. (3) Marion & Thornton, problem 2-41.

It is possible to do this problem in your head and just write down the answers. If you do that, then check your answers to parts (c) and (d) the following way. Assume that the woman exerts a constant force F on the ball during a time D t. Express F in terms of m, v, and D t using Newton’s 2^nd Law, then calculate the work done by the woman from F and check that it matches your result to part (c). For part (d), notice that the horizontal force the train exerts on the woman while she throws the ball is the same F as above. From that F, calculate the work done by the train on the woman while she throws the ball, and check that it equals your answer to part (d).

5. (3) Marion & Thornton, problem 2-40.

"Tangential acceleration" means the component of the acceleration in the direction of the velocity, and "normal acceleration" means the component perpendicular to the velocity. Recall part (b) of problem 1-9 on Homework #1 for the first of these. For the second, use the cross product.

6. (3) Marion & Thornton, problem 2-47.

In addition to doing the problem as stated, answer the following questions:

(b) If the particle has a total energy of 3 J, what are the limits of its motion in the potential?

(c) If the particle has a mass m=0.2 kg, what is its speed when it passes the point x=2 m?

7. (3) Marion & Thornton, problem 2-49.

8. (4) Marion & Thornton, problem 2-22.