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?
One postion has an area smaller the other, so it must have a force larger than the other.
Area1*force1=pressure=Area2*force2
You have the area/forces reversed, and you did not compute areas, the areas are proportional to the square of radius.
To solve this problem correctly, you need to consider the principles of Pascal's law, which states that when pressure is applied to an enclosed fluid, the pressure is transmitted uniformly in all directions.
In this case, the hydraulic lift consists of two connected cylinders: one with a larger piston (resting under the car) and one with a smaller piston (driven by compressed air). The force applied to the smaller piston will be transmitted to the larger piston, thus lifting the car.
To calculate the force required to lift the car using the hydraulic lift, you can use the following formula:
F1/A1 = F2/A2
Where:
F1 is the force being applied to the larger piston (unknown)
A1 is the cross-sectional area of the larger piston (0.20m radius)
F2 is the force being applied to the smaller piston (unknown)
A2 is the cross-sectional area of the smaller piston (0.04m radius)
Rearranging the formula, you can solve for F2:
F2 = (F1 * A2) / A1
Given that F1 is 15,000N, A1 is calculated as pi * (0.20m)^2, and A2 is calculated as pi * (0.04m)^2, you can plug in these values to find the force required to lift the car:
F2 = (15,000N * (pi * (0.04m)^2) / (pi * (0.20m)^2)
Simplify this equation:
F2 = (15,000N * (0.0016m^2 / 0.04m^2))
F2 = (15,000N * 0.04)
F2 = 600N
So, the correct answer is that a force of 600N must be applied to the smaller piston in order to lift the car using the hydraulic lift.