System Dynamics
System Dynamics
3rd Edition
ISBN: 9780073398068
Author: III William J. Palm
Publisher: MCG
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Chapter 7, Problem 7.1P
To determine

The force required to lift to the mass.

The distance x1.

The work done by the force f1.

Expert Solution & Answer
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Answer to Problem 7.1P

The force required to lift to the mass is 20lb.

The distance x1 is 18in.

The work done by the force f1 is 360lbin.

Explanation of Solution

Given information:

The area of the left side is 10in2, the area of right side is 30in2, the weight is 60lb the distance x2 is 6in.

Write the expression for the force required to lift the mass.

f1A1=f2A2f1=A1A2f2   ....... (1)

Here, force required to lift the mass is f1, the area of the left side is A1, the area of the right side is A2 and the force on the right side is f2.

Write the expression for the distance in the left side.

A1x1=A2x2x1=A2A1x2   ....... (2)

Here, distance in the left side is x1 and the distance moved by right piston is x2.

Write the expression for the work done by force f1.

W=f1x1   ....... (3)

Here, work done is W.

Calculation:

Substitute 60lb for f2, 10in2 for A1 and 30in2 for A2 in Equation (1).

f1=10in230in260lb=1360lb=20lb

Substitute, 10in2 for A1, 6in for x2 and 30in2 for A2 in Equation (2).

x1=30in210in26in=36in=18in

Substitute 18in for x1 and 20lb for f1 in equation (3).

W=20lb18in=360lbin.

Conclusion:

The force required to lift to the mass is 20lb.

The distance x1 is 18in.

The work done by the force f1 is 360lbin.

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Chapter 7 Solutions

System Dynamics

Ch. 7 - 7.11 Derive the expression for the capacitance of...Ch. 7 - Air flows in a certain cylindrical pipe 1 m long...Ch. 7 - Derive the expression for the linearized...Ch. 7 - Consider the cylindrical container treated in...Ch. 7 - A certain tank has a bottom area A = 20 m2. The...Ch. 7 - A certain tank has a circular bottom area A = 20...Ch. 7 - The water inflow rate to a certain tank was kept...Ch. 7 - Prob. 7.18PCh. 7 - Prob. 7.19PCh. 7 - In the liquid level system shown in Figure P7.20,...Ch. 7 - The water height in a certain tank was measured at...Ch. 7 - Derive the model for the system shown in Figure...Ch. 7 - (a) Develop a model of the two liquid heights in...Ch. 7 - Prob. 7.24PCh. 7 - Design a piston-type damper using an oil with a...Ch. 7 - Prob. 7.26PCh. 7 - 7.27 An electric motor is sometimes used to move...Ch. 7 - Prob. 7.28PCh. 7 - Prob. 7.29PCh. 7 - Figure P7.3O shows an example of a hydraulic...Ch. 7 - Prob. 7.31PCh. 7 - Prob. 7.32PCh. 7 - Prob. 7.33PCh. 7 - Prob. 7.34PCh. 7 - Prob. 7.35PCh. 7 - Prob. 7.36PCh. 7 - Prob. 7.37PCh. 7 - (a) Determine the capacitance of a spherical tank...Ch. 7 - Obtain the dynamic model of the liquid height It...Ch. 7 - Prob. 7.40PCh. 7 - Prob. 7.41PCh. 7 - Prob. 7.42PCh. 7 - Prob. 7.43PCh. 7 - Prob. 7.44PCh. 7 - Prob. 7.45PCh. 7 - The copper shaft shown in Figure P7.46 consists of...Ch. 7 - A certain radiator wall is made of copper with a...Ch. 7 - A particular house wall consists of three layers...Ch. 7 - A certain wall section is composed of a 12 in. by...Ch. 7 - Prob. 7.50PCh. 7 - Prob. 7.51PCh. 7 - A steel tank filled with water has a volume of...Ch. 7 - Prob. 7.53PCh. 7 - Prob. 7.54PCh. 7 - Prob. 7.55P
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