Question

A particle moves along line segments from the origin to the points (2, 0, 0), (2, 5, 1), (0, 5, 1), and back to the origin under the influence of the force field F(x, y, z)

Find the work done.

Answer 1

Work done = 0 J

Explanation:

work done= ∫ F. dr

=
`\int\limits^2_0 {x} \, dx` +
`\int\limits^2_2 {x} \, dx` +
`\int\limits^0_2 {x} \, dx` +
`\int\limits^0_0 {x} \, dx` +
`\int\limits^0_0 {y} \, dy` +
`\int\limits^5_0 {y} \, dy` +
`\int\limits^5_5 {y} \, dy` +
`\int\limits^0_5 {y} \, dy` +
`\int\limits^0_0 {z} \, dz` +
`\int\limits^1_0 {z} \, dz` +
`\int\limits^1_1 {z} \, dz` +
`\int\limits^0_1 {z} \, dz`

Work done= x²/2 + y²/2 + z²/2

Applying integral limits for entire pathway

Work done= 2 + 0 -2 + 0 + 0+ 25/2 - 25/2 + 0 + 1/2 + 0 - 1/2

Work done = 0 J