Which one of these statements regarding non-conservative forces is FALSE?
Select one:
a. A non-conservative force cannot have a potential energy defined for it.
b. The work done by a non-conservative force may be either positive or negative depending on the direction of motion
c. A non-conservative force always opposes motion
d. The work done by a non-conservative force depends on the distance travelled
To determine which statement regarding non-conservative forces is false, we'll examine each statement and explain the concept behind it.
a. A non-conservative force cannot have a potential energy defined for it.
This statement is true. Non-conservative forces, such as friction or air resistance, do not have potential energy associated with them. Potential energy is a property of conservative forces, which are path-independent and can be expressed as a function of position. Non-conservative forces are path-dependent and their work cannot be expressed as a change in potential energy.
b. The work done by a non-conservative force may be either positive or negative depending on the direction of motion.
This statement is true. Non-conservative forces can either do positive work or negative work, depending on the direction of motion. For example, if you push an object against the force of friction, the work done by friction is negative because it acts in the opposite direction of motion, reducing the object's kinetic energy. Conversely, if an object is moving in the direction of a non-conservative force, the work done can be positive, increasing the object's kinetic energy.
c. A non-conservative force always opposes motion.
This statement is false. While non-conservative forces often oppose motion, they don't always do so. For example, a rocket engine exerts a non-conservative force that propels a spacecraft forward. In this case, the force works in the same direction as the motion, so it doesn't oppose it.
d. The work done by a non-conservative force depends on the distance traveled.
This statement is true. The work done by a non-conservative force depends on the distance traveled, as well as other factors such as the magnitude and direction of the force. The work done by a force (W) is equal to the force (F) multiplied by the displacement (d) and the cosine of the angle between the force and displacement vectors (θ): W = F * d * cos(θ). The displacement is a measure of the distance traveled in the direction of the force.
Thus, the false statement is c. A non-conservative force always opposes motion.