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timofeeve [1]
3 years ago
8

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.
Mathematics
1 answer:
Anastasy [175]3 years ago
3 0

Answer:

Work done = 0 J

Step-by-step 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

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Therefore, the total of the living room and the kitchen is:

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