A garage lift has input and output circular pistons with diameters of 1 cm and 45 cm respectively. The lift is used to hold up a car with a weight of 1.7×103 N. What is the force on the input piston and what pressure is applied to the input piston
1.7*10^3 (1^2/45^2) = .84 N
.84/(pi 1^2) is pressure in Newtons/cm^2 in the fluid on both pistons.
To convert to Pascals divide by 10^4 cm^2/m^2
By the way, I think it is more likely that your car has a mass of 1.7 * 10^3 kg and a weight of 1.73*9.81 *10^3 = 1.7*10^4 N
To find the force on the input piston, we can use the principle of Pascal's law:
P1 = P2
Where P1 and P2 are the pressures exerted on the input and output pistons respectively, and assuming that the lift is in equilibrium.
The relationship between force and pressure is given by:
Force = Pressure × Area
Let's calculate the areas of the pistons first:
A1 = π * (diameter of input piston / 2)^2
= π * (1 cm / 2)^2
= π * 0.5^2
= π * 0.25 cm^2
A2 = π * (diameter of output piston / 2)^2
= π * (45 cm / 2)^2
= π * 22.5^2
= π * 506.25 cm^2
Since the force on the output piston is the weight of the car, we have:
Force2 = 1.7 × 10^3 N
Now, we can use the principle of Pascal's law to find the force on the input piston:
P1 = P2
Force1 / A1 = Force2 / A2
Force1 = (Force2 / A2) * A1
Let's plug in the values:
Force1 = (1.7 × 10^3 N / (π * 506.25 cm^2)) * (π * 0.25 cm^2)
= (1.7 × 10^3 N / 506.25) * 0.25 cm^2
= 0.00066 N * 0.25 cm^2
= 0.000165 N * cm^2
Therefore, the force on the input piston is 0.000165 N.
To find the pressure applied to the input piston, we can use the formula:
Pressure = Force / Area
Let's calculate the pressure on the input piston:
Pressure = Force1 / A1
= 0.000165 N / 0.25 cm^2
= 0.000165 N / 0.25 cm^2
Therefore, the pressure applied to the input piston is 0.00066 N/cm^2 (or 6.6 × 10^-4 N/cm^2).
To find the force on the input piston and the pressure applied to the input piston, we can use the principles of Pascal's law.
Pascal's law states that when there is a fluid in a confined space, pressure applied to the fluid will be transmitted equally in all directions.
We know that the weight of the car is 1.7×103 N. This is the force acting downwards on the output piston.
To find the force on the input piston, we can use the ratio of areas between the input piston and the output piston.
The formula for the force exerted on a piston is:
Force = Pressure * Area
The input piston has a diameter of 1 cm, so its radius (r1) is 1/2 cm or 0.5 cm. The output piston has a diameter of 45 cm, so its radius (r2) is 45/2 cm or 22.5 cm.
The area of the input piston is given by the formula:
Area1 = π * (r1)^2
Area2 = π * (r2)^2
Let's calculate the values:
Area1 = π * (0.5 cm)^2 ≈ 0.785 cm^2
Area2 = π * (22.5 cm)^2 ≈ 1586.16 cm^2
Now, we can calculate the force on the input piston using the ratio of areas:
Force1 = (Force2 * Area1) / Area2
Force1 = (1.7×103 N * 0.785 cm^2) / 1586.16 cm^2 ≈ 0.839 N
So, the force on the input piston is approximately 0.839 N.
To find the pressure applied to the input piston, we can use the formula:
Pressure = Force / Area
Pressure = Force1 / Area1
Pressure = 0.839 N / 0.785 cm^2 ≈ 1.069 N/cm^2
Therefore, the pressure applied to the input piston is approximately 1.069 N/cm^2.