There are two components of the gravitational force for an object on an inclined plane. What are those components and what is the direction of each of them?

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The question asks for the two components of the gravitational force acting on an object on an inclined plane and the directions of those components.
Option a: mg sin θ horizontal and mg cos θ vertical. This is incorrect because gravity is not resolved into horizontal and vertical components relative to the incline; instead, we resolve relative to the plane. The components along and perpendicular to the plane are the relevant ones, not horizontal/vertical components.
Option b: mg sin θ vertical and mg cos θ horizontal. This option also uses vertical/horizontal directions, which are not the natural axes for an inclined plane analysis. The standard decomposition uses axes parallel and perpendicular to the plane, so this framing is misleading and wrong.
Option c: mg sin θ perpendicular to the plane and mg cos θ parallel to the plane. Here the sin and cos assignments are swapped relative to the conventional decomposition: the component perpendicular to the plane is mg cos θ, not mg sin θ, and the component parallel to the plane is mg sin θ, not mg cos θ. Therefore this option misidentifies both the direction and the magnitude relationship.
Option d: mg sin θ parallel to the plane and mg cos θ perpendicular to the plane. This aligns with the correct vector resolution: the component along the plane (which drives sliding) is mg sin θ, and the component perpendicular to the plane (which contributes to the normal force) is mg cos θ. The directions correspond to the standard incline-plane decomposition and match the geometric projections of gravity onto the plane's axes.
In summary, options a and b fail because they use horizontal/vertical axes rather than plane-parallel/perpendicular axes, option c swaps the sin/cos roles and misassigns directions, while option d correctly assigns mg sin θ to the parallel direction and mg cos θ to the perpendicular direction, consistent with the geometry of an inclined plane.

UCIC 202503 PHYS101 Quiz 2

There are two components of the gravitational force for an object on an inclined plane. What are those components and what is the direction of each of them?

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