Given that the small piston has a radius of 0.0330 meters^2 and the large piston has a radius of 4.00 meters^2.
(a) What force will the large piston provide if the small piston is pushed down with a force of 17.0 N?.
(b) If the small piston is slowly depressed a distance of y1 = 0.300 m, by how much will the large piston rise?
(c) How much work was done in pushing down the small piston? How much work was done by the large piston?
To solve this problem, we need to apply Pascal's law, which states that the pressure applied to an enclosed fluid is transmitted uniformly throughout the fluid. This law allows us to calculate the force and displacement in a hydraulic system.
(a) To find the force exerted by the large piston, we can use the formula for pressure:
Pressure = Force / Area
Let's first calculate the area of the small piston:
Area_small = π * (radius_small)^2
= 3.14 * (0.0330 m)^2
Next, we can calculate the pressure exerted by the small piston:
Pressure_small = Force_small / Area_small
= 17.0 N / (3.14 * (0.0330 m)^2)
Now, we can calculate the force exerted by the large piston using the pressure exerted by the small piston and the area of the large piston:
Pressure_large = Pressure_small
Force_large = Pressure_large * Area_large
= Pressure_small * Area_large
= Pressure_small * π * (radius_large)^2
= Pressure_small * 3.14 * (4.00 m)^2
Substituting the values:
Force_large = (17.0 N / (3.14 * (0.0330 m)^2)) * 3.14 * (4.00 m)^2
(b) To find how much the large piston will rise, we need to calculate the displacement of the small piston:
y1 = 0.300 m
According to Pascal's law, the change in height of the large piston will be the same as the change in height of the small piston. Therefore, the large piston will also rise by a distance of 0.300 m.
(c) To find the work done in pushing down the small piston, we can use the formula for work:
Work = Force * Distance
Since the force and distance are given as follows:
Force_small = 17.0 N
Distance_small = y1 = 0.300 m
We can plug in these values to calculate the work done on the small piston:
Work_small = Force_small * Distance_small
To calculate the work done by the large piston, we can use the force exerted by the large piston and the distance it rises:
Force_large (obtained from part a)
Distance_large = y1 = 0.300 m
We can plug in these values to calculate the work done by the large piston:
Work_large = Force_large * Distance_large
By substituting the respective values in these equations, you can calculate the work done by both pistons.