Change the chapter
Question
How much pressure is transmitted in the hydraulic system considered in Example 11.6? Express your answer in pascals and in atmospheres. Example 11.6 Consider the automobile hydraulic system shown in Figure 11.13. A force of 100 N is applied to the brake pedal, which acts on the cylinder—called the master—through a lever. A force of 500 N is exerted on the master cylinder. Pressure created in the master cylinder is transmitted to four so-called slave cylinders. The master cylinder has a diameter of 0.500 cm, and each slave cylinder has a diameter of 2.50 cm.
Question Image
<b>Figure 11.13</b> Hydraulic brakes use Pascal’s principle.
Figure 11.13 Hydraulic brakes use Pascal’s principle.
Question by OpenStax is licensed under CC BY 4.0.
$2.5\times 10^{7}\textrm{ Pa}$
$2.5\times 10^{7}\textrm{ Pa} \times \dfrac{1 \textrm{ atm}}{1.013\times 10^{5}\textrm{ N/m}^2} = 147\textrm{ atm}$
Note: I forgot to express the answer in atmospheres in the video, but it's shown here in the final answer.
Solution Video

OpenStax College Physics Solution, Chapter 11, Problem 24 (Problems & Exercises) (1:07)

Sign up to view this solution video!

Rating

No votes have been submitted yet.

Quiz Mode

Why is this button here? Quiz Mode is a chance to try solving the problem first on your own before viewing the solution. One of the following will probably happen:

  1. You get the answer. Congratulations! It feels good! There might still be more to learn, and you might enjoy comparing your problem solving approach to the best practices demonstrated in the solution video.
  2. You don't get the answer. This is OK! In fact it's awesome, despite the difficult feelings you might have about it. When you don't get the answer, your mind is ready for learning. Think about how much you really want the solution! Your mind will gobble it up when it sees it. Attempting the problem is like trying to assemble the pieces of a puzzle. If you don't get the answer, the gaps in the puzzle are questions that are ready and searching to be filled. This is an active process, where your mind is turned on - learning will happen!
If you wish to show the answer immediately without having to click "Reveal Answer", you may . Quiz Mode is disabled by default, but you can check the Enable Quiz Mode checkbox when editing your profile to re-enable it any time you want. College Physics Answers cares a lot about academic integrity. Quiz Mode is encouragement to use the solutions in a way that is most beneficial for your learning.

Calculator Screenshots

OpenStax College Physics, Chapter 11, Problem 24 (PE) calculator screenshot 1
Video Transcript
This is College Physics Answers with Shaun Dychko. We need to find the pressure in this hydraulic break system. So we can find the pressure anywhere... you know, in the slave cylinders or in the master cylinder because the pressure is the same throughout— that's what Pascal's principle says— and so we'll consider the pressure created by the master cylinder because we have information about it. We know that 500 newtons ends up being applied to this master cylinder and the diameter is 0.500 centimeters which we convert to meters by noticing that the prefix 'centa' means times 10 to the minus 2. So pressure is force divided by that area and it's a circular cross-section here— this cylinder is circular— and so the area is π times its radius squared and its radius is half its diameter so I have written d over 2 here and squared and then this works out to 4 times the force divided by π times the diameter squared. That's 4 times 500 newtons divided by π times 0.500 times 10 to the minus 2 meters squared which is 2.5 times 10 to the 7 pascals.