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Energy Conservation. And Non-Conservative Forces. Conservation of Mechanical Energy. Definition of mechanical energy:. (8-6). Using this definition and considering only conservative forces, we find. Or equivalently. Conservation of Mechanical Energy.

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energy conservation

Energy Conservation

And Non-Conservative Forces

slide2

Conservation of Mechanical Energy

Definition of mechanical energy:

(8-6)

Using this definition and considering only conservative forces, we find

Or equivalently

slide3

Conservation of Mechanical Energy

Energy conservation can make kinematics problems much easier to solve

catching a home run
Catching a Home Run

At the bottom of the 9th inning,a player hits a 0.15 kg baseball overthe outfield fence. The ball leaves the bat with a speed of 36.0 m/sand a fan in the bleachers catchesit 7.2 m above the point where itwas hit. Neglect air resistance.

(a) What is the kinetic energy Kf of the ball when caught?

(b) What is the speed vf of the ball when caught.

speed and path
Speed and Path

Energy is a scalar. The speed of the cap is vi at height yi and its speed is vf at height yf, independent of the path between the two heights.

Thus the angle at which the cap is launched does not change this result, as long as vi is large enough to carry the cap to height yf.

energy of a ball act

m

2m

h

Energy of a Ball ACT

When a ball of mass m is dropped from height h, its kinetic energy just before landing is K.

If a 2nd ball of mass 2m is dropped from height h/2, what is its kinetic energy just before landing?

(a) K/4 (b) K/2 (c) K (d) 2K (e) 4K

slide7

Non-conservative Forces

In the presence of non-conservative forces, the work done by these forces must be included in the energy calculations.

This term is equal to the energy expended in overcoming the non-conservative force (usually friction) or to the energy gained from work done by the non-conservative force.

Enc = -Wnc

galileo s pendulum act
Galileo’s Pendulum ACT

How high will the pendulum swing on the other side now?

A) h1 > h2 B) h1 = h2 C) h1 < h2

Conservation of Energy (Wnc=0)

Kinitial + Uinitial = Kfinal+Ufinal

0 + mgh1 = 0 + mgh2

h1 = h2

m

h1

h2

44

slide9

Find the Diver’s Depth

A 95.0 kg diver steps off a diving board and drops into the water, 3.00 m below. At some depth d below the water’s surface, the diver comes to rest.

If the non-conservative work done on the diver is Wnc = -5,120 J, what is the depth d?

0

0 of U

0

slide10

Judging a Putt

1

A golfer badly misjudges a putt, giving the ball an initial speed v1, which sends the ball a distance d that is only one quarter of the distance to the hole.

If the non-conservative force f due to the resistance of the grass is constant, what initial speed v2 would have been needed to putt the ball from its initial position to the hole?

slide11

Landing with a Thud

A block of mass m1 = 2.40 kg is on a horizontal table with a coefficient of friction mk = 0.450 between them and is connected to a hanging block of mass m2= 1.80 kg as shown. When the blocks are released, they move a distance d = 0.50 m, and then m2 hits the floor. Find the speed of the blocks just before m2 hits.

slide12

Potential Energy Curvesand Equipotentials

The curve of a hill or a roller coaster is itself essentially a plot of the gravitational potential energy:

slide13

Total mechanical energy

Potential Energy Curves

The potential energy curve for a mass and spring