ENGR 230 Dynamics Sections 14'1 14'3

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ENGR 230 Dynamics Sections 14.1 14.3
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Conservation of Energy

• Energy can neither be created nor destroyed
  during a process, it can only change forms.

3
Sign Convention for Work

• Work done by a system is positive.
• Work done on a system is negative.
• Heat Transfer to a system is positive.
• Heat Transfer from a system is negative.

4
Work along a Path
5
Constant Force along a straight line
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Work of a Weight
7
Work done by a Spring
8
Sign for Spring Work

• Spring work is positive if the force on the
  spring and the displacement are in the same
  direction.
• Spring work is negative if the force on the
  spring and the displacement are in opposite
  directions.

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Principle of Work and Energy
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Lecture Example A frictionless car with a mass
of 1 kg is hooked to a spring (k10 N/m) on an
incline plane with a slope of 1/5. If the car is
pulled back 0.5 m from its initial position and
released, how fast is the car moving when it
passes through the point where the spring is at
rest.
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Problem 14-10 The 0.5 kg ball of negligible
size is fired up the vertical circular track.
The plunger keeps the spring compressed 0.08m
when s0. Determine how far the spring must be
pulled back and released so that the ball will
leave the track at ? 135.
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Problem 14-3 The 20-kg crate is subjected to a
force having a constant direction and a magnitude
F100N. When s15m, the crate is moving at 8
m/s. Determine the speed when s 25 m. The
coefficient of friction is µk 0.25
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What about this problem on an incline?
14

• Determine the amount of additional power
  required to accelerate a 1300-kg car from 30 to
  60 km/h on an uphill road with a 50 m rise per
  1000 m run in 20 sec. Assume a linear
  acceleration.

15

• A river flowing steadily at a rate of 240 m3/s
  is considered for hydroelectric power generation.
  It is determined that a dam can be built to
  collect water and release it from an elevation
  difference of 50 m to generate power. Determine
  how much power can be generated from this river
  water after the dam is built.