The force in Newtons on a particle directed along the x-axis is given by F (x) = exp ( - (x/2) + 6) for x≥0 where x is in meters. The particle is constrained to move along the x-axis. Find the work done in Joules on the particle, W, in moving it from x=0 to x=1 using the fact that F=dW/dx. For your reference, 1 Joule = 1 Newton * 1 meter.,

Question

Helen Tapia

Physics

10 October, 13:48

The force in Newtons on a particle directed along the x-axis is given by F (x) = exp ( - (x/2) + 6) for x≥0 where x is in meters. The particle is constrained to move along the x-axis. Find the work done in Joules on the particle, W, in moving it from x=0 to x=1 using the fact that F=dW/dx. For your reference, 1 Joule = 1 Newton * 1 meter.,

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Howard Knapp · Answer 1

To find the work done on the particle, the following is the solution:

Dw = F dx

W = integral over the path (F (x) dx)

W = integral from 0 to 1 (e^ (-x/5 + 5) dx)

W = - 5e^ (-x/5 + 5) from 0 to 1

W = 135 J

The work done is 135 J.