A ball is falling through the air. It has just two forces acting on it, its weight and air resistance. Which of the following statements is true?
a. There are only conservative forces acting on the ball.
b. There are only nonconservative forces acting on the ball.
c. There are neither conservative nor nonconservative forces acting on the ball.
d. There are both conservative and nonconservative forces acting on the ball.
All of the following statements are true except one. Which one is false?
a. Work done by a conservative force only depends on the initial and final states.
b. One can never associate a potential energy function with a conservative force.
c. An example of a nonconservative force is friction.
d. Work done by a nonconservative force depends on the path taken.
A point of stable equilibrium
a. has a force that points back toward that point regardless of how you leave it.
b. has a potential energy curve that has a maximum at that point.
c. has a potential energy curve that has a negative slope at that point.
d. is impossible.
To answer these questions, let's break down each option and explain the concepts involved:
1. For the first question:
- Conservative forces are those for which the work done is independent of the path taken, only depending on the initial and final states.
- Nonconservative forces are those for which the work done depends on the path taken.
- Weight is a conservative force because it always acts downwards and the work done only depends on the change in height of the object.
- Air resistance is a nonconservative force because it depends on the velocity and direction of the object, leading to different amounts of work done for different paths.
- Therefore, the correct answer is option d. There are both conservative (weight) and nonconservative (air resistance) forces acting on the falling ball.
2. For the second question:
- The concept of work done by conservative and nonconservative forces can help us determine the false statement.
- Conservative forces have associated potential energy functions, and the work done by them only depends on the initial and final states.
- Nonconservative forces, such as friction or air resistance, do not have associated potential energy functions, and the work done by them depends on the path taken.
- Therefore, the false statement is option b. One can never associate a potential energy function with a conservative force.
3. For the third question:
- A point of stable equilibrium refers to a condition where an object is in balance, and any small perturbation will cause it to return to its original position.
- In the context of potential energy, a stable equilibrium point corresponds to a minimum of the potential energy curve, not a maximum.
- Therefore, the false statement is option b. A point of stable equilibrium does not have a maximum potential energy.