The area of a large piston is 4.25cm^2. The area of a small piston is 0.5cm^2. What force must be applied to the small piston to lift a total weight of 1800N?

Question

The area of a large piston is 4.25cm^2. The area of a small piston is 0.5cm^2. What force must be applied to the small piston to lift a total weight of 1800N?

Answer 1

To solve this problem, we can use Pascal's principle, which states that the pressure exerted at any point of a confined fluid is transmitted undiminished in all directions throughout the fluid.

We'll first find the pressure exerted on the larger piston by the weight. Then, using Pascal's principle, we can find the force required on the smaller piston to lift the weight.

Here are the steps:

1. Calculate the pressure exerted by the weight on the larger piston: Pressure=Force Area of large piston Pressure=Area of large piston Force​ Pressure=1800 N4.25 cm2Pressure=4.25 cm21800 N​
2. Use Pascal's principle to find the force required on the smaller piston: Since pressure is transmitted equally in all directions, the pressure on the smaller piston will be the same as the pressure on the larger piston: Pressure=Force on small piston Area of small piston Pressure=Area of small piston Force on small piston​
3. Rearrange the equation to solve for the force on the small piston: Force on small piston=Pressure×Area of small pistonForce on small piston=Pressure×Area of small piston
4. Let's calculate it.
5. First, let's calculate the pressure exerted by the weight on the larger piston:
6. Pressure=1800 N4.25 cm2Pressure=4.25cm21800N​
7. Pressure≈423.529 N/cm2Pressure≈423.529N/cm2
8. Now, using Pascal's principle, we can find the force required on the smaller piston:
9. Force on small piston=Pressure × Area of small piston Force on small piston=Pressure × Area of small piston
10. Force on small piston=423.529 N/cm2×0.5 cm2Force on small piston=423.529N/cm2×0.5cm2
11. Force on small piston≈211.765 N Force on small piston≈211.765N
12. So, the force that must be applied to the small piston to lift a total weight of 1800 N is approximately 211.765 N.