Concept explainers
To allow a car to slow down or stop, hydraulic brakes transmit forces from a master cylinder to the brake pads through a fluid. Imagine this system as a tube filled with an incompressible fluid and a piston on each end. A force of 95.0 N is applied to a piston 2.65 cm in diameter on one end of the tube. a. What is the magnitude of the force that is exerted on the piston 5.15 cm in diameter on the other side? b. If the 2.65-cm piston is displaced by 1.00 cm, by how much is the 5.15-cm piston displaced?
(a)
Magnitude of force that is exerted on the piston on the other side.
Answer to Problem 40PQ
The magnitude of the force exerted on the piston on the other side is
Explanation of Solution
Pascal’s law states that pressure applied to a point of the fluid is transmitted equally and undiminished throughout the fluid. Therefore the pressure at either ends of the piston is equal.
Here,
Write the equation to find
Here,
Write the equation to find
Here,
Equate equations (I) and (II) and solve for
Write the equation to find the area of cross-section of end 1.
Here,
Write the equation to find the cross- section of end 2.
Here,
Write the equation to find
Here,
Write the equation to find
Here,
Conclusion:
Substitute
Substitute
Substitute
Therefore, the magnitude of the force exerted on the piston on the other side is
(b)
Displacement of
Answer to Problem 40PQ
The
Explanation of Solution
The fluid used in the brakes of automobiles are incompressible. So the volume of fluid displaced by the first piston must be equal to the volume of fluid displaced by second piston.
Here,
Write the equation to find
Here,
Write the equation to find
Here,
Substitute equations (VIII) and (IX) in above equation and solve for
Conclusion:
Substitute
Substitute
Substitute
Therefore, the
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