Solids

A simple model of elasticity

Objectives

• Describe the deformation of a solid in response to a tension or compression.

What’s the point?

• How do solids react when deformed?

Structure of Solids

• Atoms and molecules connected by chemical bonds

• Considerable force needed to deform

compression tension

Structure of SolidsAtoms are always “attracting each other when they are a little distance apart, but repelling upon being squeezed into one another”

distance

force

0

equil

apart

toward

apartequil

Structure of SolidsAtoms are always “attracting each other when they are a little distance apart, but repelling upon being squeezed into one another”

distance

force

0

equil

apart

toward

Force and Distance

distance

force0

equil

apart

toward

Elasticity of Solids

Small deformations are proportional to force

small stretch larger stretch

Hooke’s Law: ut tensio, sic vis (as the pull, so the stretch)

Robert Hooke, 1635–1703

Hooke’s Law GraphF

orce

exe

rted

by

the

sprin

g

Displacement from equilibrium position

0

0

slope < 0

forw

ard

back

war

d

forwardbackward

Hooke’s Law Formula

F = force exerted by the spring

k = spring constant; units: N/m; k > 0

x = displacement from equilibrium position

negative sign: force opposes distortion

F = –kx

Poll Question

forward

backward

Displacement

Spring’s Force

What direction of force is needed to hold the object (against the spring) at its plotted displacement?

A. Forward (right).

B. Backward (left).

C. No force (zero).

D. Can’t tell.

forwardbackward

Group Work

A spring stretches 4 cm when a load of 10 N is suspended from it. How much will the combined springs stretch if another identical spring also supports the load as in a and b?

Hint: what is the load on each spring?Another hint: draw force diagrams for each load.

0 N10 N

10 N0 N

Work to Deform a Spring

• To pull a distance x from equilibrium

x

kxforce

displacement

kx212

=

slope = k

area = W

• Work = F·x ;12 F = kx

• Work = kx·x12

Potential Energy of a Spring

The potential energy of a stretched or compressed spring is equal to the work needed to stretch or compress it from its rest length.

PE = 1/2 kx2

The PE is positive for both positive and negative x.

Group Poll Question

Two springs are gradually stretched to the same final tension. One spring is twice as stiff as the other: k2 = 2k1.Which spring has the most work done on it?

A. The stiffer spring (k = 2k1).

B. The softer spring (k = k1).

C. Equal for both.

Reading for Next Time

• Vibrations

• Big ideas:– Interplay between Hooke’s force law and

Newton’s laws of motion– New vocabulary that will also apply to waves

A Word