A car of mass 1420 kg rests on a hydraulic lift with a piston of radius 0.26 m that is connected to a second piston of radius 0.032 m. If the car is just barely lifted off the ground, what is the force at the second piston?
1420g*/force second=.26^2/.032^2
solve for force second
Thank you!
To find the force at the second piston, we can first calculate the pressure inside the hydraulic lift.
The pressure inside the hydraulic lift is the same at both pistons, according to Pascal's law. We can use the formula:
P1/A1 = P2/A2
Where P1 and P2 are the pressures at the first and second pistons, respectively, and A1 and A2 are the areas of the pistons.
Given:
P1 = unknown
P2 = atmospheric pressure (assumed to be 1 atm)
A1 = π * r1^2 (r1 is the radius of the first piston)
A2 = π * r2^2 (r2 is the radius of the second piston)
We are given that the car is just barely lifted off the ground, meaning the force exerted by the car's weight is balanced by the force applied at the second piston due to the hydraulic lift. Therefore, the force at the second piston is equal to the weight of the car:
F2 = m * g
Where m is the mass of the car and g is the acceleration due to gravity (approximately 9.8 m/s^2).
Given:
m = 1420 kg
To find the force at the second piston, we can follow these steps:
1. Calculate the area of the first piston (A1) using the given radius.
2. Calculate the area of the second piston (A2) using the given radius.
3. Calculate the unknown pressure at the first piston (P1) using the formula P1/A1 = P2/A2.
4. Calculate the force at the second piston (F2) using the formula F2 = m * g.