An object rests on an inclined slope. Which of the following statements is true?

Question

BlackTom AI · Accepted Answer

We start by restating the problem context: an object rests on an inclined slope, and we are asked which statement is true. However, the provided data shows there are no answer options listed, even though the answer field refers to option "d. The net force acting on the object is equal to zero."

Given the lack of options, we cannot map a specific choice to a statement and evaluate it directly. Instead, we can reason about the physics involved and the typical true/false basis for such questions.

Key concept: on an incline, gravity has a component along the slope equal to m g sin(theta) pulling the object downward along the plane, and a perpendicular component m g cos(theta) pressing the object into the surface. The net force along the incline determines whether the object accelerates down the slope or remains at rest.

- If the object is at rest and static friction is sufficient to balance the downslope component of gravity, the net force along the incline is zero. In this case, f_s = m g sin(theta) and the object does not accelerate.
- If the object is at rest but static friction is not sufficient (or if there is no friction in the scenario), the object would slide, and the net force along the incline would be nonzero (specifically, m g sin(theta) minus the kinetic friction if sliding occurs).
- If the object is moving with kinetic friction balancing the downslope component (which is a special case and depends on the coefficient of kinetic friction), the net force along the incline could again be zero, resulting in constant velocity.
- In most textbook statements, a true claim about the net force being zero on an incline typically refers to the static equilibrium case where static friction exactly cancels the downslope gravitational component, or a dynamic equilibrium case with kinetic friction balancing gravity.

Therefore, any option asserting that the net force along the incline is zero would implicitly be describing a special equilibrium condition (either static equilibrium with sufficient static friction, or a dynamic equilibrium with kinetic friction balancing the gravitational component). Conversely, an option claiming that there is a net force along the incline equal to m g sin(theta) (or any nonzero value) would be incorrect unless friction is absent or insufficient.

Because the actual list of answer options is missing, we cannot assess each choice individually. The reasoning above highlights how the true/false nature of a statement about the net force on an incline depends on whether friction is present and whether the object is at rest or in motion.

In summary, the physical truth hinges on whether the frictional force balances the downslope component of gravity. If it does (static or kinetic balance), the net force along the incline is zero; if it does not, the net force is nonzero and the object accelerates downslope.

An object rests on an inclined slope. Which of the following statements is true?

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