Final answer:
If a 10N force is applied to a 10 cm^2 piston in a hydraulic system, and the force is transmitted to a piston with an area of 100 cm^2, the force at the larger piston will be increased by a factor of 10, resulting in an output force of 100N.
Step-by-step explanation:
The question relates to the principle of hydraulics and Pascal's Law, specifically the multiplication of force via a hydraulic system. According to Pascal's Law, pressure applied to a confined fluid is transmitted undiminished throughout the fluid, exerting equal pressure on all equal areas of the containing vessel. In a hydraulic system, if you apply a force to a piston with a certain area, and this force is transmitted to another piston with a larger area, the force is multiplied according to the ratio of the two pistons' areas.
So, when a 10N force is applied to a 10 cm2 piston, and this force is transmitted to another piston with an area of 100 cm2, the force is multiplied by the ratio of the areas. Here the ratio is 100/10, which equals 10. Hence, the force exerted on the larger piston will be 10 times greater, resulting in a 100N force. This scenario applies provided the pistons are at the same vertical height and friction is negligible.
By understanding this principle, one can explain the functioning of various hydraulic devices, such as automobile brake systems, where a small force applied at the brake pedal is converted into a much larger force at the wheel cylinders, thereby enabling effective braking.