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Forces cause motion by acting on objects, and the net force determines the resulting acceleration. When multiple forces act on an object, they combine vectorially to produce a net force. This net force is the vector sum of all external forces acting on the object.

The direction and magnitude of the net force dictate the direction and rate of acceleration, as described by Newton's second law of motion. The net force is calculated by resolving each force into its x- and y-components and summing these components to find the resultant force vector. The mechanical advantage of a system is determined by the ratio of the output force to the input force.

In an ideal machine, this mechanical advantage is equal to the ratio of the input distance to the output distance. This relationship is derived from the principle of conservation of energy, which states that the work done on the input side must equal the work done on the output side. If the mechanical advantage is greater than one, the system amplifies the input force, but the distance over which the force is applied is reduced.

Conversely, if the mechanical advantage is less than one, the system reduces the input force but increases the distance over which it is applied. Friction and other non-ideal factors reduce the efficiency of a machine, meaning the actual mechanical advantage is less than the ideal mechanical advantage. The efficiency of a machine is the ratio of the actual mechanical advantage to the ideal mechanical advantage.

This efficiency accounts for energy losses due to friction, deformation, and wear. In practical applications, the actual mechanical advantage is determined by measuring the input and output forces directly. The efficiency of a compound machine, which consists of multiple simple machines, is the product of the efficiencies of each individual machine in the system.