Work, Energy, and Energy Conservation
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Transcript of Work, Energy, and Energy Conservation
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Work, Energy, and Energy Conservation
Chapter 5, Sections 1 - 3
Pg. 168-186
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WorkWork
W=∑Fd
Any force that causes a displacement on an object does work (W) on that object.
ΣF
d
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Work is done only when components of a force are parallel to a displacement.
W=∑Fd(cos θ)
WorkWork
F
θ
d
ΣF
Work is expressed in Newton • meters (N•m) = Joules (J)
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Sample Problem
How much work is done on a box pulled 3.0 m by a force of 50.0 N at an angle of 30.0° above the horizontal?
W=∑Fd(cos θ)
50.0 N
30.0°
d
ΣF
= (50.0 N x 3.0 m)(cos 30.0°)
W = 130 J
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EnergyEnergy
Two types of Energy:
1. Kinetic Energy (KE) - energy of an object due to its motion
2. Potential Energy (PE) - energy associated with an object due to the position of the object.
Energy is the ability to do work.
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Kinetic EnergyKinetic Energy
Kinetic energy depends on the speed and the mass of the object.
KE = ½ mv²
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Sample Problem
What is the kinetic energy of a 0.15 kg baseball moving at a speed of 38.8 m/s?
KE = ½ mv²
KE = (½)(0.15 kg)(38.8m/s)²
KE = 113 J
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Work-Kinetic Energy Theorem
The net work done on an object is equal to the change in kinetic energy of an object.
Wnet = ΔKE
Wnet = ½mvf ² - ½mvi²
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Sample Problem
A 50 kg sled is being pulled horizontally across an icy surface. After being pulled 15 m starting from rest, it’s speed is 4.0 m/s. What is the net force acting on the sled?
Wnet = ½mvf ² - ½mvi²
Vi = 0 m/s Vf = 4.0 m/s
∑Fd = ½mvf ²
∑F = (½mvf ²)/d = [(½)(50kg)(4.0m/s)²]/ 15 m
∑F ≈ 27 N
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Potential EnergyPotential Energy
Potential energy (PE) is often referred to as stored energy.
Gravitational potential energy (PEg) depends on the height (h) of the object relative to the ground.
PEg= mgh
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Sample Problem
What is the gravitational potential energy of a 0.25 kg water balloon at a height of 12.0 m?
PEg= mgh
PEg= (0.25 kg)(9.81 m/s²)(12.0 m)
PEg= 29.4 J
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Conservation of Mechanical Energy
Law of conservation of energy: Energy is neither created or destroyed. It simply changes form.
Mechanical energy (ME) is the sum of kinetic and all forms of potential energy.
ME = KE +∑PE
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h
100 % PE
0 % KE
50 % PE
50 % KE
0 % PE
100 % KE
Total mechanical energy remains constant in the absence of friction.
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Sample Problem
Starting from rest, a child zooms down a frictionless slide from an initial height of 3.00 m. What is the child’s speed at the bottom of the slide? The child’s mass is 25.0 kg.
hi = 3.00 mm = 25.0 kg
hf = 0 m
vi = 0 m/s
vf = ? m/s
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½ mvi² + mghi = ½ mvf² +mghf
(25.0 kg) (9.81 m/s²) (3.00 m) = (½)(25.0 kg) (Vf)²
736 J / (12.5 kg) = Vf ²
Vf ² = 58.9 m²/s² Vf = 7.67 m/s
hi = 3.00 mm = 25.0 kg
hf = 0 m
vi = 0 m/s
vf = ? m/s
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Mechanical Energy in the presence of friction
In the presence of friction, measured energy values at start and end points will differ.
f Fapp
KE
KE
KE
KETotal energy, however, will remain conserved.