HW#8: Work and Energy (Due 11 pm central time, 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
Kinetic energy in 1D, 2D, 3D
Work in 1D
Work-Energy Theorem
Work in 2D, 3D & Dot product
Example for work in 2D
Work by multiple forces
Last class…
Today…
Conservative vs. Non-conservative forces
Gravitational Potential Energy
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1
For 2D, 3D motion…
Kinetic energy
K .E . =
1 2 1
mv = m ( vx2 + v y2 + vz2 )
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2
3
Work done by a constant force
W = F d cos θ F ,d ≡ F id
magnitude
Scalar (dot) product
(B2, Ch7, Sec.3)
Force
θ
Displacement
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2
Math Review: Scalar (dot) product
A B cos θ A, B
θ = 180o
Æ
Ai B = − A B
+A B
Ai B = Bi A,
(A + B)iC = AiC + BiC
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More Example for work in 2D
Work, scalar product, angle
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
F2
vi
F1
Displacement
F3
vf
d
Wnet = Fnet id = ( F1 + F2 + F3 + ...)id
= F1 id + F2 i d + F3 id + ... = W1 + W2 + W3 + ...
= K f − Ki =
1 2 1 2
mv f − mvi
2
2
Æ Work-Energy Theorem
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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 mechanical energy?
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Conservative force
Work done by a gravity force
h1
h3
h2
h4
h1
+
-
vs.
+
+
Fg = mg
h4
(Work along h1->h2->h3->h4) = (Work along h1->h4)=mg(h1-h4)
Work done by a conservative force depends
only on the initial and final positions.
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5
Non-Conservative force
Work done by a friction force
x1
x3
-
x2
-
vs.
x1
-
x4
Fk = µk FN
x4
: opposite to
displacement
-
(Work along x1Æx2Æx3Æx4) ≠ (Work along x1Æx4)
Work done by a non-conservative force depends
on the path from initial to final position.
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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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