Engineering Mechanics: Statics & Dynamics (14th Edition)

Published by Pearson
ISBN 10: 0133915425
ISBN 13: 978-0-13391-542-6

Chapter 14 - Kinetics of a Particle: Work and Energy - Section 14.3 - Principle of Work and Energy for a System of Particles - Problems - Page 195: 2



Work Step by Step

We can determine the car's maximum penetration in the barrier as follows: $T_1+\Sigma U_{1\rightarrow 2}=T_2$ $\frac{1}{2}mv_1^2-\int_0^{x_{max}}90(10^3)x^{\frac{1}{2}dx}=\frac{1}{2}mv_2^2$ We plug in the known values to obtain: $\frac{1}{2}(\frac{4000}{32.2})(75)^2-90(10^3)x^{\frac{1}{2}}(\frac{x^{3/2}}{3/2})|_0^{x_{max}}=\frac{1}{2}(\frac{4000}{32.2})(0)^2$ This simplifies to: $x_{max}=3.24ft$
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