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
Want to see more full solutions like this?
Chapter 15 Solutions
EBK PHYSICS FOR SCIENTISTS AND ENGINEER
- In an immersion measurement of a woman's density, she is found to have a mass of 62.0 kg in air and an apparent mass of 0.0850 kg when completely submerged with lungs empty. (a) What mass of water does she displace? (b) What is her volume? (c) Calculate her density. (d) If her lung capacity is 1.75 L is she able to float without treading water with her lungs filled with air?arrow_forwardWater is flowing through a pipe that has a constriction opening into a region with a wider cross-sectional area. If the pipe regions are cylindrical with radii of 0.10 m and 0.35 m, respectively, and the water is moving with a speed of 1.50 m/s in the wider section, what is the speed of the water in the constricted section?arrow_forward(a) What is the density of a woman who floats in freshwater with 4.00% of her volume above the surface? This could be measured by placing her in a tank with marks on the side to measure how much water she displaces when floating and when held under water (briefly). (b) What percent of her volume is above the surface when she floats in seawater?arrow_forward
- (a) How high will water rise in a glass capillary tube with a 0.500-mm radius? (b) How much gravitational potential energy does the water gain? (c) Discuss possible sources of this energy.arrow_forward(a) What is the fluid speed in a fire hose with a 9.00-cm diameter carrying 80.0 L of water per second? (b) What is the flow rate in cubic meters per second? (c) Would your answers be different if salt water replaced the fresh water in the fire hose?arrow_forward(a) Calculate the absolute pressure at an ocean depth of 1 000 m. Assume the density of seawater is 1 030 kg/m3 and the air above exerts a pressure of 101.3 kPa. (b) At this depth, what is the buoyant force on a spherical submarine having a diameter of 5.00 m?arrow_forward
- A 50.0-kg woman wearing high-heeled shoes is invited into a home in which the kitchen has vinyl floor covering. The heel on each shoe is circular and has a radius of 0.500 cm. (a) If the woman balances on one heel, what pressure does she exert on the floor? (b) Should the homeowner be concerned? Explain your answer.arrow_forwardYou are pumping up a bicycle tire with a hand pump, the piston of which has a 2.00-cm radius. (a) What force in newtons must you exert to create a pressure of 6.90105 Pa (b) What is unreasonable about this (a) result? (c) Which premises are unreasonable or inconsistent?arrow_forward
- Physics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage LearningPrinciples of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningCollege PhysicsPhysicsISBN:9781938168000Author:Paul Peter Urone, Roger HinrichsPublisher:OpenStax College