a 15000N car on a hydrolyic lift rests on a cylinder with a piston of radius 0.20M,. if a connecting cylinder with a piston of 0.04M radius is driven by compressed air, what force must be applied to the smaller piston in order to lift the car?
am i doing this right?
(0.04M / 0.20M)* 15000N = 3000N
is this right, if not how do i go about getting the right anwser?
It is not right. The force required is proportional to the piston area, not the radius.
15000/(0.2)^2 = F/(0.04)^2
F = (1/5)^2 * 15,000 = 600 N
If 15,000 N weight of a car is lifting up with 0.04m diameter of piston B,the
pressure developed in the system due to the force of 300 N acting on the piston A.
Calculate the area and diameter of piston A.
W2
calculate the pressure developed in the system
with respect to the force of 300 N.
To calculate the force required to lift the car, you need to use Pascal's law, which states that pressure is transmitted uniformly in all directions in a fluid.
Here's how you can calculate the force required:
1. Determine the area of the larger piston (A₁) using the formula: A₁ = π * r₁², where r₁ is the radius of the larger piston.
A₁ = π * (0.20m)² = 0.1257 m²
2. Determine the area of the smaller piston (A₂) using the same formula: A₂ = π * r₂², where r₂ is the radius of the smaller piston.
A₂ = π * (0.04m)² = 0.005 m²
3. Now, you can calculate the force required to lift the car (F₂) using the formula: F₂ = (A₁ / A₂) * F₁, where F₁ is the weight of the car.
F₂ = (0.1257 m² / 0.005 m²) * 15000N
= 3142.86N
So, the correct force required to lift the car is approximately 3142.86N, not 3000N as calculated earlier.
To find the force that must be applied to the smaller piston in order to lift the car, you need to use Pascal's law, which states that the pressure applied to a fluid in a closed system is transmitted equally in all directions.
Here's how you can calculate the force correctly:
1. Determine the pressure on the piston of the larger cylinder:
Pressure = Force / Area
Area = π * radius^2
Area of the larger piston = π * (0.20M)^2
2. Calculate the pressure:
Pressure = Force / Area
Pressure on the larger piston = 15000N / (π * (0.20M)^2)
3. Use Pascal's law to find the force on the smaller piston:
Force on the smaller piston = Pressure * Area
Area of the smaller piston = π * (0.04M)^2
Force on the smaller piston = Pressure on the larger piston * Area of the smaller piston
Plug in the calculated values:
Force on the smaller piston = (15000N / (π * (0.20M)^2)) * (π * (0.04M)^2)
Now you can simplify the equation and solve to find the force on the smaller piston.