Potential Energy
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Transcript of Potential Energy
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Potential Energy
Gravitational and elastic
§ 7.1–7.2
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Potential Energy
The energy of relative position of two objects
gravity
springs
electric charges
chemical bonds
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Potential Energy
Energy is stored doing work against a potential
Potential energy increases when “the potential” does negative (< 0 ) work
• lifting a weight
• stretching a spring
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Gravitational Potential Energy
Gravitational potential energy =
the work to raise an object to a height
Ug = mgh
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Elastic Potential Energy
Elastic potential energy =
the work to stretch or compress a spring
Uel = 1/2 kx2
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Hooke’s Law Potential
Source: Young and Freedman, Figure 7.14.
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Gravity Doing Negative Work
Source: Young and Freedman, Figure 7.2b.
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Work from Potential Energy
When a potential does >0 work on a body:
• The body’s potential energy decreases
• The body’s kinetic energy increases
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Poll Question
When a cute furry animal moves upward in free-fall:
A. Its gravitational potential energy increases.
B. Its kinetic energy increases.
C. Both A and B.
D. Neither A nor B.
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Gravity Doing Positive Work
Source: Young and Freedman, Figure 7.2a.
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Poll Question
When a disgusting slimy thing moves downward in free-fall:
A. Its gravitational potential energy increases.
B. Its kinetic energy increases.
C. Both A and B.
D. Neither A nor B.
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Board Work Problem
A 50-g egg released from rest from the roof of a 30-m tall building falls to the ground. Its fall is observed by a student on the roof of the building, who uses coordinates with origin at the roof, and by a student on the ground, who uses coordinates with origin at the ground. What values do the two students find for:
a) Initial gravitational potential energy Ugrav 0?
b) Final gravitational potential energy Ugrav f?
c) Change in gravitational potential energy Ugrav?
d) Kinetic energy just before impact Kf?
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Forces and potentials
The (–) spatial derivative of a potential energy function is the force from that interaction.
Fx = –dU/dx Fy = –dU/dy FZ = –dU/dz
(This is Calculus 3 stuff)
Gravity –d(mgh)/dh = –mg
Elastic –d(1/2 kx2)/dx = –kx
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Mechanical Energy
The energy available to do work
Kinetic + potential = K + U
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Conservation of Mechanical Energy
• If the only force doing work is gravity, mechanical energy does not change.
E1 = E2
K1 + Ug1 = K2 + Ug2
1/2 mv12 + mgy1 = 1/2 mv2
2 + mgy2