4) When using a hydraulic system, the smaller piston has an area of .25 m2 and is pressed with a force of 185.0 N. If the larger piston is 1.33 m2 in area, how much force does it feel?
Fluid Pressure
The term fluid pressure is coined as, the measurement of the force per unit area of a given surface of a closed container. It is a branch of physics that helps to study the properties of fluid under various conditions of force.
Gauge Pressure
Pressure is the physical force acting per unit area on a body; the applied force is perpendicular to the surface of the object per unit area. The air around us at sea level exerts a pressure (atmospheric pressure) of about 14.7 psi but this doesn’t seem to bother anyone as the bodily fluids are constantly pushing outwards with the same force but if one swims down into the ocean a few feet below the surface one can notice the difference, there is increased pressure on the eardrum, this is due to an increase in hydrostatic pressure.
![**Hydraulic System Force Calculation**
When using a hydraulic system, the smaller piston has an area of 0.25 m² and is pressed with a force of 185.0 N. If the larger piston has an area of 1.33 m², how much force does it feel?
**Explanation:**
A hydraulic system works on the principle of Pascal's law, which states that pressure applied to a confined fluid is transmitted undiminished in every direction throughout the fluid.
To find the force exerted on the larger piston, we use the formula for pressure:
\[ \text{Pressure} (P) = \frac{\text{Force} (F)}{\text{Area} (A)} \]
Since the pressure is constant throughout the system:
\[ P_1 = P_2 \]
Thus,
\[ \frac{F_1}{A_1} = \frac{F_2}{A_2} \]
Given:
- \( F_1 = 185.0 \, N \)
- \( A_1 = 0.25 \, m² \)
- \( A_2 = 1.33 \, m² \)
We need to find \( F_2 \).
\[ \frac{185.0}{0.25} = \frac{F_2}{1.33} \]
Solve for \( F_2 \):
\[ F_2 = \frac{185.0 \times 1.33}{0.25} \]
Through calculation, determine the value of \( F_2 \). This will give the force experienced by the larger piston.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fcb5737f3-732a-43fa-86ea-f34b025981a9%2F047983ba-5593-45f5-8ab8-8524076cd92c%2F0cbie9c_processed.jpeg&w=3840&q=75)
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