(a) Find the force P that must be applied to a piston of area 10.60 cm2 to produce sufficient fluid pressure to support a car weighing 12,101 N by means of a column of fluid of cross sectional area 285 cm2 as seen in the figure below.
F1/A1=F2/A2 F1=F2*A1/A2
12101*10.6/285 =450N
(b) Find the increase in the car's gravitational potential energy when it is raised 1.00 m.
(c) How far must the smaller piston move in order for the larger one to move 1.00 m?
(d) Calculate the work done by P in moving the smaller piston.
To solve part (b), we can use the formula for gravitational potential energy.
Gravitational potential energy can be calculated using the formula: PE = mgh, where m is the mass of the object, g is the acceleration due to gravity, and h is the height or distance moved vertically.
In this case, we are given the weight of the car as 12,101 N. To convert this to mass, we can divide by the acceleration due to gravity, which is approximately 9.8 m/s^2.
So, the mass of the car can be calculated as follows:
Mass (m) = Weight (W) / Acceleration due to gravity (g)
= 12,101 N / 9.8 m/s^2
≈ 1237.65 kg
Next, we need to calculate the increase in height or distance (h) the car is raised, which is given as 1.00 m.
Now, we can calculate the increase in gravitational potential energy using the formula:
ΔPE = mgh
= 1237.65 kg * 9.8 m/s^2 * 1.00 m
≈ 12,112.37 J
Therefore, the increase in the car's gravitational potential energy when it is raised 1.00 m is approximately 12,112.37 J.
Moving on to part (c),
To find how far the smaller piston must move in order for the larger one to move 1.00 m, we can use the principle of Pascal's law.
According to Pascal's law, the pressure exerted on a fluid is transmitted equally in all directions. This means that the pressure applied to the smaller piston will be transmitted to the larger piston.
Using the equation F1/A1 = F2/A2, where F1 is the force applied to the smaller piston, and F2 is the force applied to the larger piston, and A1 and A2 represent the cross-sectional areas of the two pistons respectively.
We know the force applied to the larger piston is equal to the weight of the car, which is 12,101 N and the cross-sectional area of the larger piston is 285 cm^2.
We also know the cross-sectional area of the smaller piston is 10.60 cm^2.
Now, substituting the given values into the equation, we can solve for the force applied to the smaller piston (F1):
F1/A1 = F2/A2
F1/10.60 cm^2 = 12,101 N/285 cm^2
Simplifying the equation:
F1 = (12,101 N * 10.60 cm^2) / 285 cm^2
F1 ≈ 450.8 N
Therefore, the force applied to the smaller piston is approximately 450.8 N.
Finally, for part (d),
To calculate the work done by the applied force (P) in moving the smaller piston, we can use the formula:
Work (W) = Force (F) * Distance (d) * cos(θ), where θ is the angle between the force and the direction of motion.
In this case, since the applied force is in the same direction as the motion, θ = 0 degrees, and cos(0) = 1.
We are not given the distance moved by the smaller piston in the question. Therefore, we cannot directly calculate the work done.