Question

A car on a 25-m2 hydraulic lift platform weighs 15,000 N. If the force on the smaller piston required to lift it is 1/100 its weight, what is the area of the smaller piston?

Answer 1

In a hydraulic lift, the force exerted on the smaller piston is determined by the ratio of the areas of the smaller and larger pistons. The area of the smaller piston in this case is 150 m².

Step-by-step explanation:

In a hydraulic lift, the force exerted on the smaller piston is determined by the ratio of the areas of the smaller and larger pistons. According to Pascal's principle, this force is calculated using the equation:

F1/A1 = F2/A2

Given that the force on the smaller piston is 1/100 of the weight of the car, and the weight of the car is 15,000 N, we can substitute these values into the equation and solve for the area of the smaller piston:

F1/A1 = 15,000 N/100

Thus, the area of the smaller piston is 150 m2.

Answer 2

The area is 2.5 m²

Step-by-step explanation:

Step 1: Data given

A car has a 25 m² hydraulic lift platform that weighs 15000 N

The smaller piston required a force to lift = 1/100 its weight

Step 2: Calculate the area of the smaller piston

Pressure = Force / Area

F1 / A1 = F2 / A2

⇒ with F1 = weight of the hydraulic lift = 15000 N

⇒ with A1 = area of the hydraulic lift = 25 m²

⇒ with F2 = 1/100 of it's weight = 1500 N

A2 = F2 / (F1/A1)

A2 = 1500 ( 1500/25)

A2 = 2.5

The area is 2.5 m²