# Several forces act on the particle define the work w

This preview shows pages 11–15. Sign up to view the full content.

Several forces act on the particle. Define the work W done on the particle by a force F x for this trajectory, by W = Z x f x i F x dx Note: “W” stands for work, do not get confused with “weight” Units, in SI system: 1 Joule = 1 J = 1 N.m (same as K and U)

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Phys 2A - Mechanics Comments: Work can be defined for any one force acting on the particle, or for a sum of some forces, or even for the net force. One must simply be specific as to which it is. The time dependence of the trajectory, x=x(t), is irrelevant: Note that we may need to specify x(t) to compute work, but the result does not depend on it (so there may be many other forces acting on the particle dictating the actual time dependence in x=x(t)). Work depends on the trajectory itself, through: initial and final points the path followed: for example W = Z x f x i F x dx = Z t f t i F x dx dt dt = Z t f t i F x v x dt x i x f no the same as x i x f
Phys 2A - Mechanics Examples: 1a. What is the work done by the gravitational force on a 20 kg box carried vertically up from y i =1.0m to y f =5.0m? W = Z y f y i F grav ,y dy = Z y f y i ( - mg ) dy = - mg ( y f - y i ) Notice that the box was moved arbitrarily, not thrown upwards! W = - (20)(9 . 8)(5 - 1) J = - 784 J ANS: 1b. What is the work done by the gravitational force on a 20 kg box carried vertically down from y i =5.0m to y f =1.0m? W = - (20)(9 . 8)(1 - 5) J = +784 J

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
Phys 2A - Mechanics 2a. The same box is pushed against a 2.0 N/m spring to compress it from x=0.0cm to x=-5.0 cm. What is the work done by the spring? ANS: The choice of coordinate axis is implicit instatement of problem. So W = Z x f x i F spring ,x dx = Z x f x i ( - kx ) dx = - 1 2 k ( x 2 f - x 2 i ) W = - 1 2 (2 . 0)(( - 5 . 0) 2 - (0) 2 ) J = - 25 J Notice,again, that the box was moved arbitrarily, pushed by hand!
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• 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.

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

• 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.

Dana University of Pennsylvania ‘17, Course Hero Intern

• 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.

Jill Tulane University ‘16, Course Hero Intern