Conervative Force Conervation of Energ force i conervative if the work done b the force from r to r, but depend on initial and final poition onl Conervative Non-conervative Section #4.5 #4.6 Conervation of Energ Potential Energ If all force acting on a particle are conervative, then the um of kinetic and potential energ i contant: Hibbeler textbook notation for conervation of energ: Potential energ due to gravit: PE gravit Wh where W h mgh Potential Energ Potential energ due to pring where PE pring pring contant (lb/in, lb/, N/m, N/mm) pring deflection amount of tretch (+) or amount of compreion (-) of pring from untretched or untrained length Work Energ Dnamic Definition If there are non-conervative force that do work, then the work-energ equation i in 64, the common non-conervative force i occur in other coure be careful to not double count a force in both the PE and W categorie
Example Problem # 4000 lb vehicle i traveling up the 0 degree lope at a peed of 60 /ec. What frictional force mut be applied at the tire/road urface to top the vehicle in 75 feet? 75 0º Example Problem # v 5 /ec 0 feet he 4000 lb cart i carried b four frictionle wheel that roll on the loping urface. In the poition hown the velocit i 5 /ec. What i the pring tiffne, K, if the cart i topped aer compreing the pring 6 inche? K Example Problem #a Goal: Find pring tiffne K Given: v + 5, v 0, ume: No friction Draw: 0 feet K x Example Problem #b Solution: + PE KE PE 4000lb KE mv 5. PE Wh KE + PE
Example Problem # n 8-lb collar can lide without friction along a vertical rod. he collar i releaed from ret in the poition hown with the pring untretched. Determine the velocit of the collar aer it ha moved a) 4 inche b) 7.5 inche Example Problem #4 6 lb collar can lide without friction on a vertical rod. he collar i puhed down to compre the pring 8 inche and i then releaed. Determine the maximum height reached b the collar from the uncompreed poition and the maximum velocit of the collar. Note that the pring i not attached to the collar.
Example Problem #5 lock and are releaed from ret with an untretched pring. Determine the velocit of aer it ha moved 0.5 ; the maximum velocit of block, and the maximum diplacement of block. ume no friction. Example Problem #5a - Kinematic x Example Problem #5b Given: lb K 0, ume: No friction Goal: v, 0, x, 0 v 0,, 0 W 8 lb, W lb,, State : find v, given, 0. 5 State : find max v, a, 0 State 4: find max, 4 v, 4 0 Example Problem #5 State#a Equation: Solution: + PE KE + PE KE + PE KE4 PE4 KE mv, + mv, 0 PE + Kx, + W, 0 + 0 0 Example Problem #5 Example Problem #5 State #a State : find max v, a, 0 Static equilibrium! F K F K Wlb 4
Example Problem #5 State #b PE + Kx, + W + PE KE PE,, x, 0. 60 Example Problem #5 State#4 PE 4 + Kx,4 + W + PE KE4 PE4,4 x, 4,4 KE 0lb v g 4,4 0 Example Problem #6 W lb W 0 lb Example Problem #6a lock i attached b a light pulle to block. lock C ret on, but lide freel on the cable. ll block are releaed from ret. lock fall through a hole in the bracket which top block C. How far doe block decend below the bracket? W C 8 lb C Goal: Given: er dropping feet, how far below bracket doe block drop before tarting back up? W lb, W 0 lb, W C 0 lb, v, v, vc, 0, ume: No friction, datum line for each weight at initial poition Equation: Example Problem #6b Solution: State : initial poition KE 0 PE 0 State : C hit bracket Draw: C C C Example Problem #6c PE PE W W WC 0 + 0 + + v + g g g ( )( W W W ) C 5
Example Problem #6c State : jut aer C top at bracket KE. lb + 0lb ( m v + m v ) 6. ( )( W W ) ( )( lb ) PE 0lb v v 6. State 4: topped at max ditance below bracket PE 4 KE 4 0 Example Problem #6d + PE KE4 PE4 Ditance block drop below the bracket: Check b ΣFma W m a W W m a + m a W W a a m + m W W + W m a W W 0lb lb a a g.. 9 W W + lb + 0lb 6