{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

w4_elevator - W done by the force F x in moving a particle...

Info icon This preview shows page 1. Sign up to view the full content.

View Full Document Right Arrow Icon
1 Problem. Going up? When a body moves a distance d along a straight line as a result of being acted on by a force of constant magnitude F in the direction of motion, then the work W done by the force is W = Fd . We will generalize the definition of work to the case of variable force. Given a force function F ( x ) defined and continuous at each point x of the straight line segment [ a, b ] , we will define the work W done by this variable force in moving a particle along the x -axis from the point x = a to the point x = b . Partition the interval [ a, b ] into n subintervals with the same length Δ x . Choose an arbitrary point c k in the k ’th interval [ x k - 1 , x k ] . Approximate the work Δ W k done by the force from the point x = x k - 1 to the point x = x k by Δ W k F ( c k x. We approximate the total work by summing from 1 to n , so W n k =1 F ( c k x. This is a Riemann sum for F ( x ) . When Δ x 0 , the sum approaches the definite integral of F ( x ) from a to b . Therefore, we are motivated to define the work
Image of page 1
This is the end of the preview. Sign up to access the rest of the document.

Unformatted text preview: W done by the force F ( x ) in moving a particle from a to b to be Z b a F ( x ) dx . Problem. An electric elevator with a motor at the top has a multistrand cable weighing 2 kg/m. When the car is at the first floor, then 60 meters of cable are paid out. When the car is at the top floor, then effectively meters are paid out. a) What is the force exerted by the motor to just lift the cable? Hint: Newton’s second law says that the force is equal to mass times acceleration, F = ma , with units measured in Newtons [N=kg · m/s 2 ]. You may take the free gravitational accelera-tion to be g = 10m/s 2 . b) How much work does the motor do just lifting the cable when it takes the car from the first floor to the top?...
View Full Document

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern