Question

The force on an object, acting along the x axis, varies asshown. Determine the work done by the force to move the object (a)from x=0.0 to x=10.0m, and (b) fromx=0.0 to x=15.0m.

Answer 1

W = F^→ ∙ Δx^→

The work done on the particle in this figure is the area under the curve.

(a)   

Area under the curve from x = 0.0 to x = 10.0 m:

A _{(x=0 to x=10)}

                        = ½ (4 m + 10 m) × 400 N

                        = ½ (14 m) × 400 N

                        = 2800 J

∴ The work done by this force to move the particle from x = 0.0 to x = 10.0 m along the x-axis is 2800 J.

(b)   

Area under the curve from x = 0.0 to x = 15.0 m:

A _{(x=0 to x=15)}    = A _{(x=0 to x=10)} + [A _{(x=10 to x=15)}]

    

A _{(x=10 to x=15)}   = ½ (5 m + 2 m) × -200 N

                        = ½ (7 m) × -200 N

                        = -700 J

A _{(x=0 to x=15)}    = A _{(x=0 to x=10)} + [A _{(x=10 to x=15)}]

                        = 2800 J – 700 J

                        = 2100 J

∴ The work done by this force to move the particle from x = 0.0 to x = 15.0 m along the x-axis is 2100 J.