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Potential Energy
Gravitational and elastic
§ 7.1–7.2
Potential Energy
The energy of relative position of two objects
gravity
springs
electric charges
chemical bonds
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
Gravitational Potential Energy
Gravitational potential energy =
the work to raise an object to a height
Ug = mgh
Elastic Potential Energy
Elastic potential energy =
the work to stretch or compress a spring
Uel = 1/2 kx2
Hooke’s Law Potential
Source: Young and Freedman, Figure 7.14.
Gravity Doing Negative Work
Source: Young and Freedman, Figure 7.2b.
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
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.
Gravity Doing Positive Work
Source: Young and Freedman, Figure 7.2a.
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.
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?
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
Mechanical Energy
The energy available to do work
Kinetic + potential = K + U
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