Conservation of Energy

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Letitia Brooks
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1 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

2 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

3 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.

4 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, Example Problem #5 Example Problem #5 State #a State : find max v, a, 0 Static equilibrium! F K F K Wlb 4

5 Example Problem #5 State #b PE + Kx, + W + PE KE PE,, x, 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 v + g g g ( )( W W W ) C 5

6 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

PROBLEMS ON WORK AND ENERGY PRINCIPLE

PROBLEMS ON WORK AND ENERGY PRINCIPLE PROLEMS ON WORK ND ENERGY PRINCIPLE PROLEMS. he.8 kg collar lide with negligible friction on the fixed rod in the vertical plane. If the collar tart from ret at under the action of the contant 8-N horizontal