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