Explanation Draw the free body diagram of the cup filled with liquid at a height h as in Figure 1. Express the surface area on the inside of the cup using the theorem of Pappus and Guldinus. A = ∑ θ r ¯ L (I) Here, the angle of revolution measured in radians is θ , the perpendicular distance from the axis of revolution to the centroid of the composite part is r ¯ , and the length of the composite part is L . Since the angle of revolution is measured in radians, θ = 2 π rad Substitute 2 π rad for θ in Equation (I). A = 2 π ∑ [ r ¯ L ] (II) Refer to Figure 1 and calculate the value of x . x = 20 h 50 = 2 h 5 (III) Calculate the total surface area of the cup. A = 2 π ∑ r ¯ L (IV) Conclusion: Refer to Figure (1) and use a spreadsheet to calculate the value of L , r ¯ , and r ¯ L for two segments as shown in Table 1. Segment L ( mm ) r ¯ ( mm ) r ¯ L ( mm 2 ) 1 20 2 + 50 2 = 53.85 20 1077.033 2 10 5 50 ∑ 1127.03 Refer to Table (1), Substitute 1 , 127.03 mm 2 for ∑ r ¯ L in Equation (II). A = 2 π × 1 , 127.03 mm 2 = 7 , 081.357 mm 2 (V) Refer to Equation (V) and calculate the height h when liquid is poured into the cup so that it contains half the surface area on the inside of the cup. A = 1 2 ( 7 , 081.357 mm 2 ) = 3 , 540.678 mm 2 (VI) Refer to Figure (1) and use a spreadsheet to calculate the value of L , r ¯ , and r ¯ L for two segments as shown in Table 2

13th Edition

ISBN: 9780132915540

Author: Russell C. Hibbeler

Publisher: Prentice Hall

See similar textbooks

Concept explainers

Slope and Deflection

The slope in a deflected beam is described as an angle in radians made by the tangent of the section with the original axis of the beam. The deflection at any point on the axis of the beam is defined as the lateral displacement of the point before and af…

Videos

Question

Chapter 9.3, Problem 111P

To determine

The height of the liquid poured into the cup (h) .

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 9.3, Problem 110P

Chapter 9.3, Problem 112P

Students have asked these similar questions

using the theorem of three moments, find all the moments, I need concise calculations only

Practise question need help on

Can you show explaination and working. The answer from the text book is Q=5.03 X 10^-3

Chapter 9 Solutions

Engineering Mechanics: Statics

Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid (x,y) of the shaded area....Ch. 9.1 - Determine the centroid of the shaded area. Prob....Ch. 9.1 - Locate the center of mass x of the straight rod if...Ch. 9.1 - Locate the centroid of the homogeneous solid...Ch. 9.1 - Locate the centroid z of the homogeneous solid...Ch. 9.1 - Locate the center of mass of the homogeneous rod...Ch. 9.1 - Prob. 2P Ch. 9.1 - Prob. 3P Ch. 9.1 - Prob. 4P

Knowledge Booster

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, mechanical-engineering and related others by exploring similar questions and additional content below.

The height of the liquid poured into the cup ( h ) .

Solution Summary: The author explains how to determine the height of the liquid poured into the cup using the theorem of Pappus and Guldinus.

Concept explainers

Videos

The height of the liquid poured into the cup (h) .

Want to see the full answer?

Chapter 9 Solutions