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