Today: Work, Kinetic Energy, Work-Energy Theorem for 1D motion

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Motivation: Why do we learn about work and energy???

Energy : Central concept in science and engineering … and in our daily lives…

Energy transforms from one type to other, but conserved.

In Physics 102, we learn about “Mechanical Energy”.

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1 Kinetic energy Kinetic energy (K.E.): An energy associated with motion

Kinetic energy of an object of mass m and speed v

1 v KE.. K mv2 2 m Energy is a scalar quantity (No direction!)

SI Unit for energy: J (Joule) mm2 Jkg kgmNm ss22

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1 K..EK mv2 2

The heavier and the faster, the kinetic energy gets greater.

(KE of a fast baseball) vs (KE of a slow baseball) ?

(KE of a car at 60 mi/h) vs (KE of a trailer at 60 mi/h) ?

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2 iClicker

When the velocity of the object doubles, its kinetic energy ______.

(a) doubles 1 2 (b) quadruples K..EK mv (c) becomes half 2 (d) unchanged

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What makes kinetic energy change?

(1 D motion)

Fx Fnet ma net

defined as “Net Work”, W net , in 1D Change in kinetic energy is equal to the “net work”! Work-Energy Theorem K KKW f inet6

3 Definition of work by a single force, F, in 1D:

WFxF m

(Work) = (Force) x (Displacement) F

Work done by a force F on an object, the displacement of which is x .

If F and x are in the same direction, work done by F is positive.

If F and x are in the opposite direction, work done by F is negative.

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iClicker Quiz 1

Work done by a gravity on a falling elephant WFx is ______.

a) Positive b) Negative c) zero If force and displacement point the same direction, the work is ______.

Example: In this case, suppose m=1000 kg and distance = 10 m, calculate work done by gravity.

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4 iClicker Quiz2: Work done by a gravity on a ball that is going up

Gravity WFx

Displacement Is work positive, negative, zero? a) Positive b) Negative c) zero Gravity

If force and displacement point the opposite directions, the work is ______. Example: In this case, suppose m=10 kg and distance = 10 m, calculate work done by gravity. 9

Net Work when multiple forces are exerted on a single object

Wnet Fnet x

(F1 F2 F3 ...)x

F1x F2x F3x ...

W1 W2 W3 ...

Work-Energy Theorem

K f KKWinet

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5 Work-Energy Theorem

As shown for 1D motion,

K f KKWinet

Work-Energy Theorem

Positive net work: KE increases (iClicker Quiz 1)

Negative net work: KE decreases (iClicker Quiz 2)

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iClicker Quiz 1. As a sled is pulled by dogs across a flat, snow-covered field at a constant velocity, work done by the air resistance and friction is ______,

2. …and the work done by dogs is ______, 3. … and net work done on the sled is ______.

a) Positive b) Zero c) Negative d) Not enough information

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6 Example

A 5-kg object is moving at 7 m/s. A 2-N force is applied in the opposite direction of motion and then removed after the object has traveled an additional 20 m.

A) What is the initial kinetic energy? B) What is the work done by 2N force? C) What is the final kinetic energy?

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iClicker

A horizontal force of +100 N is applied in the x direction to a 20-kg object initially moving at -10 m/s in the x-direction. The object finally reaches a velocity of zero, reverses direction, and reaches +10 m/s finally. Friction force is negligible.

Assuming the 100 N force is the only force, What is the work done by the 100 N force between initial and final? a) -1000 J b) +1000 J c) +2000 J d) -2000 J e) zero

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