Question

A robot arm that controls the position of a video camera in an automated surveillance system is manipulated by a servo motor that exerts a force on a push-rod. The force is given by F(x) = (12.9 N/m2)x2 ,

where x is the position of the end of the pushrod. If the push-rod moves from x1 = 1 m to x2 = 4 m, how much work did the servo motor do? Answer in units of J.

Answer 1

W = 270.9 J

Step-by-step explanation:

given,

F(x) = (12.9 N/m²) x²

work = Force x displacement

dW = F .dx

the push-rod moves from x₁= 1 m to x₂ = 4 m

integrating the above

`\int dW = \int_(x_1)^(x_2)F. dx`

`W = \int_(x_1)^(x_2)F. dx`

`W = \int_(1)^(4) (12.9 x^2) dx`

`W = 12.9* [(x^3)/(3)]_1^4 dx`

`
`W = 12.9* [(4^3)/(3)-(1^3)/(3)] dx`

W = 270.9 J

work done by the motor is W = 270.9 J