Physics 321 -- Spring 2003
Homework #2, due Wednesday
Jan. 22
1. (2) 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. 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. (3) Marion & Thornton, problem 2-29.
An “8% grade” means that the slope = 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 Dt. Express F in terms of m, v, and Dt using Newton’s 2nd
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. (4) 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. Use the
cross product for this.
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. (2) Marion & Thornton, problem 2-49.
8. (5) Marion & Thornton, problem 2-22.