Final answer:
By using the principles of hydraulic systems and the formula for the area of a circle, the force exerted by the larger piston can be calculated when a known weight is placed on the smaller piston. Additionally, the respective movement distances of the pistons can be determined using the conservation of energy and the inverse relationship of their areas.
Step-by-step explanation:
To find the force exerted by the larger piston, we can use the principle of hydraulic systems which states that the pressure is equal throughout the system. So, the force over area ratio will remain constant for both pistons. This gives us the formula: F1/A1 = F2/A2, where F1 and A1 are the force and area of the smaller piston, and F2 and A2 of the larger.
First, we find the area of each piston using the formula for the area of a circle, A = πr². For the smaller piston with a diameter of 2.5 cm, the radius is 1.25 cm, thus A1 = π(1.25 cm)². Similarly, for the larger piston with a diameter of 30 cm, the radius is 15 cm, thus A2 = π(15 cm)². Then we calculate F1 which is the weight placed on the smaller piston: F1 = 50 kg-wt * 9.8 N/kg as 1 kg-wt is equivalent to the gravitational force on 1 kg which is 9.8 N.
The exerted force F2 on the larger piston can then be calculated from F1 and the areas. Using the conservation of energy, we can find the distance the larger piston will move by the inverse relationship of the areas of the two pistons. If the smaller piston moves through a distance s1, then the larger piston will move through a distance s2 = (A1/A2) * s1.