What is the displacement of the blue piston?

In summary, the conversation discussed investigating the relationship between the cylinder diameter and the range of motion of a piston in a hydraulic system. Two scenarios were given, one with the blue cylinder having double the diameter of the red cylinder and the other with the blue cylinder having half the diameter of the red cylinder. The displacement of the blue piston was calculated to be 8cm for the first scenario and 1.5cm for the second scenario. The method used involved equating the volume of the red cylinder's movement to the volume of the blue cylinder's movement, assuming incompressibility of the fluid.
  • #1
blue_print101
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The purpose is to investigate the relationship between the cylinder diameter and the range of motion of a piston in a hydraulic system.

The teacher didn't give any initial of final position at all, so I think the teacher means in general.

Homework Statement

What is the displacement of the blue piston?

a) If the blue cylinder has 2x the diameter of the red cylinder, and the red piston is moved a displacement of 4cm.

and

b) If the blue cylinder has 1/2x the diameter of the red cylinder, and the red piston is moved a displacement of 3cm
The attempt at a solution

a) I'm assuming the 2x means double so I did the following;

I just assumed that for example the red cylinder has a diameter of 20cm and given that the red piston of the red cylinder has a displacement of 4cm the blue cylinder would have a diameter of 40cm since it's twice the size of the red cylinder, which would double the displacement to 8cm.

Therefore I think the displacement of the blue piston would be 8 cm.b) I just supposed again, that the red cylinder has a diameter of 10 cm, Since the question tells us that the blue cylinder has half of the red cylinder, the blue cylinder's diameter would be 5cm, and since the displacement for the red piston for the red cylinder is 3cm, the displacement for the blue piston would be half also, which would be 1.5 cm.

Therefore, I think the displacement of the blue piston would be 1.5 cm.
 
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  • #2
I guess you have a two cylinder system with an incompressible fluid?

For a) you may call, generally, the diameter of the red cylinder D, and thus the diameter of blue cylinder 2D. What are the areas associated with diameters? We thus may work out the volume V=Area x distance through which the red cylinder moves. Equate this to the volume through with the blue cylinder must move (by incompressibility) by calling the distance x.

Do that same method for b).
 
  • #3


I would like to clarify a few points in this scenario. First, we need to define what is meant by "displacement" in this context. Displacement can refer to the change in position or the distance traveled by an object. Since the teacher did not specify the initial or final position of the pistons, I will assume they are referring to the change in position.

In part a), assuming the red piston has a displacement of 4cm, we need to determine the displacement of the blue piston if its diameter is twice that of the red piston. In this case, we can use the equation for the area of a circle (A = πr^2) to determine the relationship between the diameters and the displacement. If the diameter of the blue piston is 2 times that of the red piston, the area of the blue piston would be 4 times that of the red piston. This means that for every 1cm the red piston moves, the blue piston would move 4cm. Therefore, the displacement of the blue piston would be 4 times that of the red piston, which would be 16cm.

In part b), the same logic applies. If the blue cylinder has half the diameter of the red cylinder, its area would be 1/4 that of the red cylinder. This means that for every 1cm the red piston moves, the blue piston would move 1/4 cm. Therefore, the displacement of the blue piston would be 1/4 of the red piston, which would be 0.75 cm.

In conclusion, the displacement of the blue piston would be 16 cm in part a) and 0.75 cm in part b). It is important to clarify the definitions and assumptions made when solving a problem to ensure accuracy in the results. Additionally, it would be beneficial to include the initial and final positions of the pistons in the problem to provide a more complete understanding of the hydraulic system.
 

1. What is displacement?

Displacement is a physical quantity that represents the distance and direction of an object's change in position from its starting point. It is typically measured in units of length, such as meters or centimeters.

2. How is displacement different from distance?

Distance is a scalar quantity that represents the total length of the path traveled by an object. Displacement, on the other hand, is a vector quantity that takes into account the direction of the object's movement.

3. What is the formula for calculating displacement?

The formula for displacement is Δx = xf - xi, where Δx represents the displacement, xf is the final position, and xi is the initial position. This formula applies to one-dimensional motion.

4. How is displacement measured?

Displacement can be measured using various tools and techniques, depending on the object and its motion. For example, a ruler or measuring tape can be used to measure the displacement of a stationary object, while a motion sensor or GPS device can be used to measure displacement during motion.

5. What is the significance of the blue piston in displacement?

The blue piston is a hypothetical object used in physics problems to illustrate the concept of displacement. It represents a moving object with a known starting and ending position, making it easier to calculate displacement using the formula mentioned above.

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