A particle is subject to a force F_x that varies with position as shown in the f

Question

A particle is subject to a force F_x that varies with position as shown in the following figure. Find the work done by the force on the particle as it moves from x = 0 to x = 4.00 m. ____ J Find the work done by the force on the particle as it moves from x = 5.00 m to x = 6.00 m. ____ J Find the work done by the force on the particle as it moves from x = 12.0 m to x = 15.0 m. ____ J What is the total work done by the force over the distance x = 0 to x = 15.0 m? _____ J A force F^rightarrow = (3xi^Hat + 4yj^Hat), where F^rightarrow is in newtons and x and y are in meters, acts on an object as the object moves in the x direction from the origin to x = 4.58 m. Find the work W = integral F^rightarrow middot dr^rightarrow done by the force on the object. _____ J

Explanation / Answer

here,

work done = area under the force vs displacement curve

a)

for x = 0 to x = 4 m

W = 0.5 * ( 3 - 0) * ( 4 - 0)

W = 6 J

b)

for x = 5 m to x = 6 m

W = ( 6 - 5) * ( 3 - 0)

W = 3 J

c)

for x = 12 m to x = 15 m

work done , W = 0.5 * ( 15 - 12) * ( 1.5 - 0)

W = 2.25 J

d)

the total work done , W = 0.5 * 3 * 5 + (10 - 5) * 3 + 0.5 * ( 15 - 10) * 3

W = 30 J

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