Physics

Problem

A block is released from rest on a rough plane that is inclined at

30^{\circ}

above the horizontal. Which choice of coordinate axes will most simplify writing Newton’s second-law equations for the block’s motion? a)

x

-axis horizontal and

y

-axis vertical b)

x

-axis parallel to the plane (down the slope) and

y

-axis perpendicular to the plane c)

x

-axis perpendicular to the plane (upward) and

y

-axis parallel to the plane (up the slope) d)

x

-axis parallel to the plane (up the slope) and

y

-axis perpendicular to the plane

Intuitive explanation

The key is choosing axes that align with the natural directions of motion and forces rather than fighting against them. On an inclined plane, the block accelerates along the slope while the normal force acts perpendicular to it—so tilting your axes to match the plane (one parallel to the surface, one perpendicular) eliminates the need to decompose the normal force and lets gravity do most of the work in just one direction. This cuts your algebra roughly in half compared to using horizontal and vertical axes.

Intuitive explanation

Browse the problem library