High School

Consider the figure above, taken from a Webassign homework problem on Fluids. The small piston has a cross-sectional area of 2 cm\(^2\), and the large piston has a cross-sectional area of 200 cm\(^2\). The force \(F_1\) applied at the small piston is 196 Newtons. What maximum mass can be lifted at the large piston?

A. 0.02 kg
B. 8000 kg
C. 19600 N
D. 2000 kg

Answer :

The maximum mass that can be lifted at the large piston is 19,600 N / 9.8 m/s² = 2000 kg.

The maximum mass that can be lifted at the large piston can be determined by comparing the forces acting on both pistons. According to Pascal's principle, the pressure applied to an enclosed fluid is transmitted undiminished to all parts of the fluid and the walls of the container.

In this case, the force acting on the small piston (F₁) is transmitted to the large piston. The force exerted by the large piston (F₂) can be calculated using the equation: F₂ = F₁ × (A₂ / A₁), where A₁ and A₂ are the cross-sectional areas of the small and large pistons, respectively.

Substituting the given values, we have F₂ = 196 N × (200 cm² / 2 cm²) = 19,600 N. Since force is equal to mass multiplied by acceleration (F = m × g), we can calculate the maximum mass that can be lifted using the equation: m = F₂ / g, where g is the acceleration due to gravity (approximately 9.8 m/s²).

To know more about piston refer here:

https://brainly.com/question/14866490#

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