This preview shows pages 1–3. Sign up to view the full content.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
Unformatted text preview: Kinetic Energy, Work, and Power Shina Tan Kinetic energy of a single particle The th particle in a system of n particles obeys Newtons Second Law m r ( t ) = F ( t ) , (1) where F ( t ) = F ( e ) ( t ) + f ( t ), F ( e ) ( t ) is the force exterted by objects external to the system, and f ( t ) is the force exterted by the th particle in the system. Taking the scalor products of both sides of Eq. (1) with the instantaneous velocity v ( t ) = r ( t ) , and noting that d dt h 1 2 m v 2 ( t ) i = d dt h 1 2 m v ( t ) v ( t ) i = 1 2 m v ( t ) v ( t ) + 1 2 m v ( t ) v ( t ) = m v ( t ) v ( t ) = m r ( t ) v ( t ) , we get d dt h 1 2 m v 2 ( t ) i = F ( t ) d r ( t ) dt . The left hand side is the rate of change of the kinetic energy, and the right hand side F ( t ) v ( t ) is called the power exerted on the particle. Integrating this equation over time from t 1 to t 2 , we get 1 2 m v 2 ( t 2 ) 1 2 m v 2 ( t 1 ) = Z t 2 t 1 F ( t ) d r ( t ) . (2) The left hand side is the change of the kinetice energy 1 2 m v 2 , and the right hand side is the work done on the particle. 1 Kinetic energy of a system of particles Definition 1 The kinetic energy of a system of particles is defined as T ( t ) = X 1 2 m v 2 ( t ) . (3)...
View Full
Document
 Spring '11
 Tan
 mechanics, Energy, Force, Kinetic Energy, Power, Work

Click to edit the document details