c. N Use EqualU ves from x, = 0 to xf-35ng the block as the bloc ,\" s on an obj

Question

c. N Use EqualU ves from x, = 0 to xf-35ng the block as the bloc ," s on an object tho 4.000x2i-6.000) N forc actson 29, NAforce F = ( acc moves 550.0 m along the direction pointin from the positive y axis. Find the work done object as it moves along the path. eby the force on 9-6 F 36. N 30, A particle moves in the xy plane (Fig. P9.30) from the origin to a point having 2 (7.0) 7.00,4.00 Pro 37. coordinates x = 7.00 m andy = 4.00 m under the influence of a force given by F = 3 +x). a. N What is the work 0 done on the particle by the force F if it moves along path 1 (shown in red)? FIGURE P9.30 b. N What is the work done on the particle by the force Fift c. N What is the work done on the particle by the force Fifit d. C Is the force F conservative or nonconservative? Expln. springs of the same length moves along path 2 (shown in blue)? d- 21 moves along path 3 (shown in green)'? ct. 11 A A inot ic attached to two

Explanation / Answer

29. given, force F = 4x^2i - 6yj N

displacement of the object r = 550(cos(22.5)i + sin(22.5)j)

hence work done by the force = F.r

at time t, let the position of the particel be x, y

then y/x = tan(22.5)

and, work done in this process, dW = F.dr = F.(dxi + dyj)

dW = 4x^2*dx - 6ydy

now, dy = tan(22.5)dx

hence

dW = 4x^2*dx - 6x*tan^2(22.5)dx

dW = (4x^2 - 1.029x)dx

integrating from x = 0 to x = x

W = 4x^3/3 - 1.029x^2/2

now final x = 550cos(22.5) = 508.1337

hence

W = 174801383.05271 J

hence work done by the force on the object W = 174.801*10-^6 J

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