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A 57.0 kg cheerleader uses an oil-filled hydraulic lift to hold four 110 kg football players at a height of 1.20 m. The diameter of the cheerleader's piston What is the diameter of the football players' piston if the cheerleader and football players are at is 16.0 cm. the same height?

User Samrat Das
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Final answer:

The question is a Physics problem about a cheerleader using a hydraulic lift to balance football players, requiring calculation of the football players' piston diameter using principles of fluid mechanics and Pascal's Principle.

Step-by-step explanation:

The question involves a cheerleader using a hydraulic lift to hold football players, which is a concept from Physics involving principles of fluid mechanics and Pascal's Principle. The scenario describes a situation where the cheerleader's piston is lifting a heavier load (football players) at the same height using a hydraulic system. To find the diameter of the football players' piston, the principle of hydraulic systems that states the product of pressure and area (force) is constant can be used:

Let d1 be the diameter of the cheerleader's piston and d2 the diameter of the football players' piston.

F1 = m1 × g is the force the cheerleader exerts on her piston, where m1 is the cheerleader's mass and g is the acceleration due to gravity (9.8 m/s2).

F2 = m2 × g is the force needed to hold the football players at the specified height, where m2 is the combined mass of the four football players.

According to Pascal's Principle:

F1 / A1 = F2 / A2

Where A1 = π(d1/2)^2 and A2 = π(d2/2)^2 are the areas of the cheerleader's and football players' pistons respectively.

By rearranging the equation and solving for d2, we can find the diameter of the football players' piston

User Ankit Sachan
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