Piston 1 has a diameter of 0.524cm Piston 2 has a diameter of 5.64 cm. In the absence of friction, determine the force required on piston 1 necessary to support an object, m, with weight 1072 N. (Neglect the height difference between the bottom of the two pistons, and assume that the pistons are massless)
The pressure is the same.
Force1/Area1=Force2/area2
figure the area of each (area=PI (diameter/2)^2)
Is the 1072N=F2?
yes.
So F1/2.15E-5=1072N/2.4E-3
F1= 2.15E-5*(1072/2.4E-3)
F1=9.63E10 N
I think I did this right but the answer comes up wrong when I submit it
To determine the force required on piston 1, we can use the principles of fluid pressure in a hydraulic system. According to Pascal's law, the pressure exerted by a fluid at any point is transmitted equally in all directions.
Step 1: Find the respective areas of the pistons.
The area of a piston can be calculated using the formula:
Area = π * (radius)^2
Given that the diameter of piston 1 is 0.524 cm, its radius (r1) can be calculated as:
r1 = diameter / 2 = 0.524 cm / 2 = 0.262 cm = 0.00262 m
The area of piston 1 (A1) can be calculated as:
A1 = π * (r1)^2 = π * (0.00262 m)^2
Similarly, for piston 2, the radius (r2) can be calculated as:
r2 = diameter / 2 = 5.64 cm / 2 = 2.82 cm = 0.0282 m
The area of piston 2 (A2) can be calculated as:
A2 = π * (r2)^2 = π * (0.0282 m)^2
Step 2: Calculate the pressure exerted on piston 2.
The pressure (P) exerted on piston 2 can be calculated using the formula:
P = force / area = mass * gravity / A2
Given that the weight of the object (m) is 1072 N, and neglecting the height difference and mass of the pistons, the mass can be calculated as:
mass = weight / gravity = 1072 N / 9.8 m/s^2
Now we can calculate the pressure on piston 2:
P = (1072 N / 9.8 m/s^2) / A2
Step 3: Determine the force required on piston 1.
According to Pascal's law, the pressure exerted on piston 1 will be the same as that on piston 2. Thus, we can equate the pressure on piston 2 (P) to the force (F1) required on piston 1, divided by its area (A1):
P = F1 / A1
Rearranging the equation, we can solve for F1:
F1 = P * A1
Substituting the value of P calculated in Step 2 and the respective values of A1 and A2, we can calculate the force required on piston 1.