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HW#8: and (Due 11 pm central , 11/4, Tuesday).

HW hint will be posted on course web (http://web.njit.edu/~kenahn) Prof. Ahn will be on travel for a workshop during Nov. 6th -9th. Prof. George Georgiou will give the lecture on Nov. 7th, Friday (same room, same time).

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Work and Energy in 1D, 2D, 3D Work in 1D Work-Energy Theorem Last class… Work in 2D, 3D & Example for work in 2D Today… Work by multiple Conservative vs. Non-conservative forces Gravitational

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1 For 2D, 3D

Kinetic energy

112 222 KEmvmvvv..==()x ++yz 22

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Work done by a constant WFd=≡ cosθFd, Fdi

Scalar (dot) product magnitude (B2, Ch7, Sec.3) Force

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2 Math Review: (dot) product ABcosθ A,B

o θ =180 Æ AiBAB=− + A B

AiiBBA=+=+, ( ABCACBC ) iii

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More Example for work in 2D

Work, scalar product,

iClicker Quiz What is the work done on the block? (a) 6 J (b) 12 J (c) 14 J (d) 15 J (e) 22 J

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3 Work with multiple forces on a single object F 1 vi v f F2 Displacement d F3 WFdFFF==+++ii( ...) d net net 123 =+++=+++Fd123iii Fd Fd... W 123 W W ...

1122 =−=K K mv − mv Æ Work-Energy Theorem fi22 f i

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Multiple forces on a box

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4 Motivation Why do we learn about potential energy and conservation of ?

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Conservative force Work done by a force

h1 h1

h + 3 vs. + -

h2 + Fmgg = h4 h4

(Work along h1->h2->h3->h4) = (Work along h1->h4)=mg(h1-h4) Work done by a depends only on the initial and final positions.

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5 Non-Conservative force

Work done by a force

x1 x3 x2 x4

- - vs. FFkkN= µ : opposite to - displacement x1 x4

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(Work along x1Æx2Æx3Æx4) ≠ (Work along x1Æx4)

Work done by a non-conservative force depends on the path from initial to final .

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Conservative forces in Phys 105: Gravity, Spring force Let’s consider spring force later...

Non-Conservative forces in Phys 105: Friction, Normal force, Tension, Other applied forces

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