Physics 321 -- Spring 2004

Homework #2, due Wednesday Jan. 28 at beginning of class

1.         [2pts] 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.         [3pts] Marion & Thornton, problem 2-26.

            Hint: Use the concepts of work and energy, rather than F=ma, to solve this problem.  In part (b), note that the total distance that the block slides across the floor is equal to (2m+x), where x is the distance the spring is compressed.

3.         [3pts] Marion & Thornton, problem 2-29.

            An “8% grade” means that the slope = 0.08.

4.         [3pts] 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) in the following way.  Assume that the woman exerts a constant force F on the ball during a time T. Express F in terms of m, v, and T using Newton’s 2^nd Law, then calculate the work done by the force 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).  Hint: How far does the woman move with respect to the ground while she is throwing the ball?

5.         [4pts] Marion & Thornton, problem 2-40.

            “Tangential acceleration” is the component of the acceleration in the direction of the velocity.  (Recall part (b) of problem 1-9 on Homework #1.)  “Normal acceleration” is the component perpendicular to the velocity.

6.         [3pts] 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 in part (b) has a mass m=0.2 kg, what is its speed when it passes the point x=3 m?

7.         [2pts] Marion & Thornton, problem 2-49.

8.         [5pts] Marion & Thornton, problem 2-22.

9.         [5pts] A ball is thrown vertically upward with an initial speed of 20 meters/second. Due to air resistance, the terminal velocity is 15 meters/second. Find the maximum height, and the time until the ball returns to its starting point, assuming the air resistance is
  (a) proportional to the velocity.
  (b) proportional to the square of the velocity.
  (c) proportional to the 3/2 power of the velocity.

            Hints:
(1) You can find the height from a first-order differential equation by writing v = dy/dt = (dy/dv)(dv/dt) and using Newton's Second Law for (dv/dt).
(2) You can set up the solution for resistance that is an arbitrary power P of the velocity, and then specialize to the cases P = 1, 1.5, 2. You could find the solutions in closed form for P=2, but in the other cases you will need to use numerical methods.

(Last updated 1/25/2004.)