# Introduction to Statics and Dynamics. Problem Book by Pratap R., Ruina A.

By Pratap R., Ruina A.

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Extra resources for Introduction to Statics and Dynamics. Problem Book

Example text

1 ı + 12ˆ 13 (−3ˆ z ˆ3 T3 λ ˆ ıˆ 27 m = 6 kg y T2 b) A good solution will clearly document and explain the computer methodology. 23, assume now that the mass at A has non-zero acceleration of (1m/s 2 )ıˆ + (2m/s 2 )ˆ + (3m/s 2 )kˆ . Find the tension in the three ropes at the instant shown. 120 A small object (mass= 2 kg) is being pulled by three strings as shown. 0kˆ m/s2 . a) Draw a free body diagram of the mass. b) Write the equation of linear momentum balance for the mass. Use λ’s as unit vectors along the strings.

A) Draw separate free body diagrams of each block, the string, and the system of the two blocks and string. b) Write separate equations for linear momentum balance for each block, the string, and the system of blocks and string. c) What is the acceleration of the center of mass of the two blocks? d) What is the force in the string? e) What is the speed of the center of mass for the two blocks after they have traveled a distance d down the slope, having started from rest. ) if the string were replaced by a massless rod?

When the particle reaches point 2, its velocity is again perpendicular to the radial direction. Determine the speed increment v which would have to be added (instantaneously) to the particle’s speed at point 2 to transfer it to the circular trajectory through point 2 (the dotted curve). Express your answer in terms of v1 . 138 Linear momentum balance for general systems with multiple interacting parts moving more or less independently reduces to F = m a if you interpret the terms correctly. What does this mean?

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