In a car lift,compressed air with a gauge pressure of 4.0 × 10⁵ Pa is used to raise a piston with a circular cross-sectional area.If the radius of the piston is 0.17 m,what is the maximum mass that can be raised using this piston?

Question

Quizplus · Accepted Answer

The force exerted on the piston is equal to the pressure multiplied by the area of the piston:

F = P × A

where F is the force, P is the pressure, and A is the area of the piston. The area of a circle is given by:

A = πr²

where r is the radius of the piston. Substituting the values given into the equations, we get:

A = π(0.17 m)² = 0.091 m²

and

F = (4.0 × 10⁵ Pa) × (0.091 m²) = 36,400 N

We can now use this force to calculate the maximum mass that can be lifted, by using the equation:

F = mg

where m is the mass and g is the acceleration due to gravity (9.81 m/s²). Solving for m, we get:

m = F/g = (36,400 N)/(9.81 m/s²) ≈ 3700 kg

Therefore, the maximum mass that can be raised using this piston is approximately 3700 kg. Option B is the correct answer.

In a Car Lift,compressed Air with a Gauge Pressure of 4.0