The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpson's Rule toestimate the work done by the force in moving an object a distance of 18 m.44.8xjoulesX03 6 9 12 15 18f(x) 9.6 9.1 8.7 8 7.7 7.5 7.2

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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When gas expands in a cylinder with radius r, the pressure P at any given time is a function of the volume V: P = P(V). The force exerted by the gas on the piston (see the figure) is the product of the pressure and the area: F = πr²P. piston head W = ·V2 V The work done by the gas when the volume expands from volume V₁ to volume V₂ is as follows. P dV X i) In a steam engine the pressure and volume of steam satisfy the equation PV1.4 = k, where k is a constant. (This is true for adiabatic expansion, that is, expansion in which there is no heat transfer between the cylinder and its surroundings.) Calculate the work done by the engine during a cycle when the steam starts at a pressure of 160 lb/in2 and a volume of 500 in3 and expands to a volume of 1000 in 3. (Round your answer to two decimal places.) W = ft-lb
The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. X 4 8 12 f(x) 5 5.5 7.3 16 20 24 28 32 36 8.8 9.4 8.3 6.9 5.1 4.3 Use the midpoint rule with n = 4 to estimate the work W (in J) done by the force in moving an object from x = 4 to x = 36. W = J
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Answer: 48 Newtons

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The table shows values of a force function f(x), where x is measured in meters and f(x) in newtons. Use Simpson's Rule to estimate the work done by the force in moving an object a distance of 18 m. 44.8 x joules X 0 3 6 9 12 15 18 f(x) 9.6 9.1 8.7 87.7 7.5 7.2