lecturenotes-Feb10

lecturenotes-Feb10 - Wab ,1 = Wab ,2 Wab ,1 = Wba ,2 Wab ,1...

Info iconThis preview shows pages 1–11. Sign up to view the full content.

View Full Document Right Arrow Icon
Background image of page 1

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

View Full DocumentRight Arrow Icon
P ave = W Δ t P = dW dt W ab ,1 = W ab ,2 W ab ,1 = W ba ,2 C-F W ab , 1 W ab , 2 Non-C-F W ab , 1 ≠− W ba , 2 P = F net v Power E mech = KE + U Δ U = W conservative F Δ E mech = 0 Potential Energy Mechanical Energy Conservation of Mechanical Energy
Background image of page 2
Potential energy Potential energy : Energy U which describes the confguration (or spatial arrangement) oF a system oF objects that exert conservative Forces on each other. It’s the stored energy in system. Gravitational Potential energy : [~associated with the state of separation] Δ U grav = mg ( ) dy = mg y f y i ( ) y i y f = mg Δ y If U grav ( y = 0) 0 then U grav ( y ) = mgy Elastic Potential energy : [~associated with the state of compression/tension of elastic object] Δ U spring = 1 2 kx f 2 1 2 kx i 2 If U spring ( x = 0) 0 then U spring ( x ) = 1 2 kx 2 Δ U = W Δ U grav if going up U grav if going down U spring if x goes or (any displacement) DeFnition
Background image of page 3

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

View Full DocumentRight Arrow Icon
Mechanical Energy Mechanical energy: Only conservative forces Isolated system : Assuming only internal forces (no external forces yet - Sec. 8.6) No external force from outside causes energy change inside E mech = KE + U W net = Δ KE Sec. 7 - 3 W conservative = −Δ U Sec. 8 -1 Δ E mech = 0 = Δ KE + U ( ) Δ KE = −Δ U
Background image of page 4
How to apply your knowledge to solve problems? When Friction is present, it always removes energy, so E(final) is less the E(initioal) E mec ( final ) = E mec ( initial ) Energy removed by work of friction K f + U f = K i + U i F f d Always think about the problem and the signs!! My preference is to always use Mechanical Energy E mec ( final ) = E mec ( initial ) K f + U f = K i + U i If there are no non-conservative forces involved,
Background image of page 5

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

View Full DocumentRight Arrow Icon
Background image of page 6
Problem 8-4: Roller Coaster What is the speed of coaster at a) Point A b) Point B c) How high will it go on the last hill?
Background image of page 7

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

View Full DocumentRight Arrow Icon
Problem 8-4: Roller Coaster What is the speed of coaster at a) Point A b) Point B c) How high will it go on the last hill? Δ U grav = mg Δ y = 0 = −Δ KE Δ KE = 1 2 m v A 2 v 0 2 ( ) v A = v 0 Δ U grav = mg Δ y = mg ( h /2 h ) = −Δ KE Δ KE = 1 2 m v B 2 v 0 2 ( ) 1 2 v B 2 v 0 2 ( ) = g h /2 ( ) v B = gh + v 0 2 Δ U grav = mg Δ y = mg ( h max h ) = −Δ KE Δ KE = 1 2 m 0 v 0 2 ( ) mg ( h max h ) = 1 2 m 0 v 0 2 ( ) h max = v 0 2 2 g + h h max
Background image of page 8
Problem 8-4: Roller Coaster: Different way What is the speed of coaster at a) Point A b) Point B c) How high will it go on the last hill? E Mech = mv o 2 2 + mgh = mv a 2 2 + mgh v a = v 0 h max E mec =E kin +U E Mech = mv 0 2 2 + mgh E Mech = mv o 2 2 + mgh = mv b 2 2 + mg h 2 v b = v 0 2 + gh E Mech = mv o 2 2 + mgh = 0 + mgh max h max = v 0 2 2 g + h
Background image of page 9

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

View Full DocumentRight Arrow Icon
slides below to give her the greatest possible speed when she reaches the bottom of the slide. Which one should she choose? 1. A
Background image of page 10
Image of page 11
This is the end of the preview. Sign up to access the rest of the document.

Page1 / 36

lecturenotes-Feb10 - Wab ,1 = Wab ,2 Wab ,1 = Wba ,2 Wab ,1...

This preview shows document pages 1 - 11. Sign up to view the full document.

View Full Document Right Arrow Icon
Ask a homework question - tutors are online