A hydraulic press has one piston of diameter 2.0cm and the other piston of diameter 8.0cm. What force (in N) must be applied to the smaller piston to lift an object of mass 700kg at the larger piston?Question 16Answera.300Nb.429Nc.600Nd.200N
Question
A hydraulic press has one piston of diameter 2.0cm and the other piston of diameter 8.0cm. What force (in N) must be applied to the smaller piston to lift an object of mass 700kg at the larger piston?Question 16Answera.300Nb.429Nc.600Nd.200N
Solution
A hydraulic press works based on Pascal's principle, which states that a change in pressure at any point in an enclosed fluid is transmitted equally throughout the fluid.
The force required can be calculated using the formula:
F1 / A1 = F2 / A2
where: F1 is the force applied on the smaller piston, A1 is the area of the smaller piston, F2 is the force on the larger piston (which is equal to the weight of the object), and A2 is the area of the larger piston.
The area of a piston can be calculated using the formula:
A = π * (d/2)²
where d is the diameter of the piston.
Given: d1 = 2.0 cm = 2.0 * 10^-2 m, d2 = 8.0 cm = 8.0 * 10^-2 m, and m = 700 kg.
The weight of the object (F2) can be calculated using the formula:
F2 = m * g
where g is the acceleration due to gravity (approximately 9.8 m/s²). So, F2 = 700 kg * 9.8 m/s² = 6860 N.
The areas of the pistons are:
A1 = π * (2.0 * 10^-2 m / 2)² = 3.14 * 10^-4 m², and A2 = π * (8.0 * 10^-2 m / 2)² = 5.02 * 10^-3 m².
Substituting these values into the formula, we get:
F1 = F2 * A1 / A2 = 6860 N * 3.14 * 10^-4 m² / 5.02 * 10^-3 m² = 428.6 N.
So, a force of approximately 429 N must be applied to the smaller piston to lift the object. The correct answer is b. 429 N.
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