7 conservation of energy
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7 Conservation of Energy. Potential Energy The Conservation of Mechanical Energy The Conservation of Energy Mass and Energy Hk: 23, 27, 39, 47, 55, 65, 69, 71. Potential Energy. Potential Energy is stored energy Potential Energy is position dependent (KE is speed dependent)

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7 Conservation of Energy

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7 conservation of energy

7 Conservation of Energy

  • Potential Energy

  • The Conservation of Mechanical Energy

  • The Conservation of Energy

  • Mass and Energy

  • Hk: 23, 27, 39, 47, 55, 65, 69, 71


Potential energy

Potential Energy

  • Potential Energy is stored energy

  • Potential Energy is position dependent (KE is speed dependent)

  • Ex. object at higher height has more PE

  • Types of PE: gravitational, elastic, electric, magnetic, chemical, nuclear.

  • /


Conservative forces

Conservative Forces

  • When the work done by a force moving from position 1 to 2 is independent of the path, the force is Conservative.

  • The work done by a Conservative Force is zero for any closed path.

  • Conservative Forces have associated Potential Energies

  • /


Non conservative forces

Non Conservative Forces

  • Produce thermal energy, e.g. friction

  • Work done by Non Conservative Forces is path dependent, e.g. longer path, more work required

  • /


Potential energy functions

Potential Energy Functions


Elastic potential energy

Elastic Potential Energy


Ex elastic potential energy

Ex. Elastic Potential Energy

  • 100N/m spring is compressed 0.2m.

  • F = -kx = -(100N/m)(0.2m) = -20N

  • U = ½kx2 = ½(100N/m)(0.2m)2 = 2J

  • /


Gravitational potential energy

Gravitational Potential Energy


Ex gravitational potential energy

Ex. Gravitational Potential Energy

  • Ex: A 2kg object experiences weight (2kg)(9.8N/kg) = 19.6N.

  • At 3m above the floor it has a stored energy of mgy:

  • (2kg)(9.8N/kg)(3m) = 48.8Nm = 48.8J.

  • /


Conservation of energy

Conservation of Energy

  • Individual energy levels change.

  • Sum of all individual energies is constant.

  • /


Conservation of mechanical energy

Conservation of Mechanical Energy


7 conservation of energy

KE

E

Ug


Ex conservation of mechanical energy object dropped from height h above floor

Ex. Conservation of Mechanical Energy: Object dropped from height h above floor.


7 conservation of energy

1

2

3


7 conservation of energy

y

y

Energies and speeds are same at height y

Accelerations at y are not same


Work energy with friction

Work Energy with Friction


7 conservation of energy

s

Example: The smaller the frictional force fk, the larger the distance, s, it will travel before stopping.


7 conservation of energy

1

5

2

4

3

A 2.00kg ball is dropped from rest from a height of 1.0m above the floor. The ball rebounds to a height of 0.500m. A movie-frame type diagram of the motion is shown below.


7 conservation of energy

By energy conservation, the sum of all energies in each column is the same, = E1 = mg(1) = 19.6J

Calculate v2: (use 1st and 2nd columns)

mg(1) = ½ m(v2)2.

g = ½ (v2)2.

v2 = 4.43m/s

Calculate PE-thermal: (use 1st and 5th columns)

mg(1) = mg(1/2) + PE-thermal

mg(1/2) = PE-thermal

PE-thermal = 9.8J


7 conservation of energy

Calculate PE-elastic: (use 1st and 3rd columns)

PE-elastic + PE-thermal = mg(1)

PE-elastic + 9.8 = 19.6

PE-elastic = 9.8J

Calculate v4: (use 1st and 4th columns)

½ m(v4)2 + PE-thermal = mg(1)

½ m(v4)2 + 9.8 = 19.6

½ m(v4)2 = 9.8

(v4)2 = 2(9.8)/2

v4 = 3.13m/s


Potential energy force

Potential Energy & Force


Equilibrium

Equilibrium

  • Stable: small displacement in any direction results in a restoring force toward Equilibrium Point

  • Unstable: small displacement in any direction results in a force away from Equilibrium Point

  • Neutral: small displacement in any direction results in zero force


Mass and energy

Mass and Energy


Efficiency thermodynamics

Efficiency & Thermodynamics


Summary

Summary

  • Potential Energy function & force

  • The Conservation of Mechanical Energy

  • The Conservation of Energy

  • Mass and Energy

  • /


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