Which of the following is true?
a. Conserved forces cannot do work
b. Work can be performed on an object without moving it
c. If the work is done by a conserved force, you do not need to know the path the object took
d. To know the total work performed on an object you must always know the path it takes.
e. Normal forces can do work
To determine which statement is true, let's examine each option and explain the reasoning behind it:
a. Conserved forces cannot do work: This statement is incorrect. Conserved forces can indeed do work. Work is defined as the transfer of energy that occurs when a force is applied over a certain distance, and conserved forces can certainly transfer energy in this way.
b. Work can be performed on an object without moving it: This statement is true. Work is not solely dependent on the displacement (or movement) of an object. Even if an object is stationary, work can still be done if a force is applied to it. For example, if you push against a wall, you are performing work despite the wall not moving.
c. If the work is done by a conserved force, you do not need to know the path the object took: This statement is true. Conserved forces, such as gravity or electrostatic forces, depend only on the initial and final positions of an object. The path the object takes between these positions does not affect the work done by these forces.
d. To know the total work performed on an object, you must always know the path it takes: This statement is incorrect. The total work done on an object is independent of the path it takes. The work done only depends on the initial and final positions and the forces involved, not on the specific trajectory.
e. Normal forces can do work: This statement is incorrect. Normal forces act perpendicular to the surface of contact between two objects and are responsible for preventing objects from interpenetrating. As they act at right angles to the displacement, they do no work on the object.
Therefore, the correct statement among the options given is:
c. If the work is done by a conserved force, you do not need to know the path the object took.