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The concept of mechanical energy conservation under the influence of conservative forces, using the example of a simple pendulum. It also discusses non-conservative forces, such as friction, and their impact on energy conservation. examples and calculations for various scenarios.
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Lecture 11
2
Conservation of Mechanical
Energy
Under the influence of conservative forces only
(i.e. no friction or drag etc.)
M.E. = K + U = constant
Note that U and K can include such things as elastic
potential energy, rotational kinetic energy, etc.
Example : simple pendulum or slippery dip
(if friction & air resistance are negligible).
KJF §10.
Example: Tarzan
Tarzan who weighs 688N swings from a cliff at the
end of a convenient vine that is 18m long. From the
top of the cliff to the bottom of the swing he descends
by 3.2m.
(a) What is his speed at the bottom of the swing?
Neglect air resistance.
(b) The vine will break if the force on the vine
exceeds 950N. Does it break at the bottom of
the swing?
[7.9 m.s–1, no]
Loop the loop
What height does the ball have to start at to make
it through the loop?
Example 1 :
Block on horizontal surface slides to rest due to kinetic
friction. Work done by friction is
∆ME = ∆ K = – F k d
Example 2 :
Block sliding along a horizontal surface at constant
velocity. If work is done AGAINST friction by an applied
force F app and Δ K & Δ U = 0 then;
The amount of thermal energy produced must be exactly
equal to the amount of work done, in other words…
Work and Friction (1)
Work and Friction (2)
Force working AGAINST friction is F appl = – F k
(why?) but F k = μk F N , cosθ = 1, and s = d , so the amount
of thermal energy produced is
∆ E th = F k d = μk F N d
Clearly, here work is not reversible. (Why not?)
Work done BY friction - same magnitude, opposite sign
A 20 kg child, starting from rest,
slides down a 3m high frictionless
slide.
How fast is he going at the
bottom?
[7.7 ms
Now he slides down a slide with friction, and his
speed at the bottom is 6.0 ms
thermal energy has been produced by friction?
[228 J]
Problem: Skier
A 60 kg skier leaves the end of a ski jump ramp with a
velocity of 24 ms
Suppose that as a result of air resistance the skier returns to
the ground with a speed of 22 ms
the hill that is 14m below the ramp.
How much energy is dissipated by air resistance during the
jump?
[11 kJ]
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