Question

A 1,200kg car is placed on a hydraulic lift. The lifting head of the hydraulic lift has an area of 50cm². If the hydraulic pump acts on a section of tube with a 1cm² area, how much force does the pump need to exert to lift the car?

Answer 1

hydraulic pump needs to exert a force of 235.2 Newtons to lift the car.

Step-by-step explanation:

To determine the force needed to lift the car, we can use Pascal's law, which states that the pressure exerted in a fluid is transmitted uniformly in all directions.

Given:

Mass of the car (m) = 1,200 kg

Area of the lifting head (A_head) = 50 cm²

Area of the hydraulic pump (A_pump) = 1 cm²

First, let's convert the areas to square meters:

A_head = 50 cm² = 50/10000 = 0.005 m²

A_pump = 1 cm² = 1/10000 = 0.0001 m²

Next, we can calculate the pressure exerted by the car on the lifting head using the formula:

Pressure = Force/Area

The force exerted by the car on the lifting head is given by:

Force = Pressure * A_head

The pressure exerted by the car is equal to the weight of the car divided by the area of the lifting head:

Pressure = (mass * gravity) / A_head

Where gravity is the acceleration due to gravity, approximately 9.8 m/s².

Substituting the given values:

Pressure = (1,200 kg * 9.8 m/s²) / 0.005 m²

Simplifying the expression:

Pressure = 2,352,000 N/m²

Now, we can calculate the force needed to lift the car using the formula:

Force = Pressure * A_pump

Substituting the given values:

Force = 2,352,000 N/m² * 0.0001 m²

Calculating the force:

Force = 235.2 N

Therefore, the hydraulic pump needs to exert a force of 235.2 Newtons to lift the car.