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How is the force on a frictionless inclined plane calculated?

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A diagram displays six types of simple machines with labeled illustrations: inclined plane, wedge, screw, lever, wheel and axle, and pulley, each shown with real-world examples like ramps, axes, screws, seesaws, door handles, and pulleys lifting objects. — simple machine Six simple machines for transforming energy into work.

An inclined plane is a simple machine consisting of a sloping surface used to raise heavy objects. When discounting friction, the force required to move an object up the incline is less than the object's actual weight.12

Mathematically, the force F required to move a block of weight W up a frictionless inclined plane is calculated by multiplying the weight by the sine of the angle (θ) that the plane makes with the horizontal. This is expressed by the equation:12

$F = W \sin θ$

As the slope of the incline becomes steeper, the required force F increases, approaching the total weight of the object.12