This document is posted to help you gain knowledge. Please leave a comment to let me know what you think about it! Share it to your friends and learn new things together.
Transcript
1
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
A deformation is the change in size or shape of an object.
An elastic object is one that returns to its original size and shape after contact forces have been removed. If the forces acting on the object are too large, the object can be permanently distorted.
3
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.1): A steel beam is placed vertically in the basement of a building to keep the floor above from sagging. The load on the beam is 5.8104 N and the length of the beam is 2.5 m, and the cross-sectional area of the beam is 7.510-3 m2. Find the vertical compression of the beam.
Force of floor on beam
Force of ceiling on beam
Y
L
A
FL
L
LY
A
F
For steel Y=200109 Pa.
m 100.1N/m 10200
m 5.2
m 105.7
N 108.5 42923
4
Y
L
A
FL
7
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.6): A 0.50 m long guitar string, of cross- sectional area 1.010-6 m2, has a Young’s modulus of 2.0109 Pa. By how much must you stretch a guitar string to obtain a tension of 20.0 N?
mm 5.0m 100.5
N/m 100.2
m 5.0
m 100.1
N 0.20
3
2926
Y
L
A
FL
L
LY
A
F
8
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
If the stress on an object exceeds the elastic limit, then the object will not return to its original length.
An object will fracture if the stress exceeds the breaking point. The ratio of maximum load to the original cross-sectional area is called tensile strength.
9
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.10): An acrobat of mass 55 kg is going to hang by her teeth from a steel wire and she does not want the wire to stretch beyond its elastic limit. The elastic limit for the wire is 2.5108 Pa. What is the minimum diameter the wire should have to support her?
Want limit elastic stress A
F
limit elasticlimit elastic
mgFA
mm 1.7m 107.1limit elastic
4
limit elastic2
3
2
mgD
mgD
11
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.25): The upper surface of a cube of gelatin, 5.0 cm on a side, is displaced by 0.64 cm by a tangential force. If the shear modulus of the gelatin is 940 Pa, what is the magnitude of the tangential force?
F
F
N 30.0cm 5.0
cm 64.0m 0025.0N/m 940 22
L
xSAF
From Hooke’s Law:
L
xS
A
F
14
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.24): An anchor, made of cast iron of bulk modulus 60.0109 Pa and a volume of 0.230 m3, is lowered over the side of a ship to the bottom of the harbor where the pressure is greater than sea level pressure by 1.75106 Pa. Find the change in the volume of the anchor.
36
9
63
m 107.6
Pa 100.60
Pa 1075.1m 23.0
B
PVV
V
VBP
17
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Simple harmonic motion (SHM) occurs when the restoring force (the force directed toward a stable equilibrium point) is proportional to the displacement from equilibrium.
19
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.28): The period of oscillation of an object in an ideal mass-spring system is 0.50 sec and the amplitude is 5.0 cm. What is the speed at the equilibrium point?
At equilibrium x=0:
222
2
1
2
1
2
1mvkxmvUKE
Since E=constant, at equilibrium (x = 0) the KE must be a maximum. Here v = vmax = A.
27
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.41): The diaphragm of a speaker has a mass of 50.0 g and responds to a signal of 2.0 kHz by moving back and forth with an amplitude of 1.810-4 m at that frequency.
(a) What is the maximum force acting on the diaphragm?
2222maxmax 42 mAffmAAmmaFF
The value is Fmax=1400 N.
29
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
A simple pendulum is constructed by attaching a mass to a thin rod or a light string. We will also assume that the amplitude of the oscillations is small.
33
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.60): A clock has a pendulum that performs one full swing every 1.0 sec. The object at the end of the string weighs 10.0 N. What is the length of the pendulum?
m 25.0
4
s 0.1m/s 8.9
4L
2
2
22
2
2
gT
g
LT
Solving for L:
36
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
Example (text problem 10.84): The gravitational potential energy of a pendulum is U=mgy. Taking y=0 at the lowest point of the swing, show that y=L(1-cos).
L
y=0
L
Lcos
)cos1( Ly
37
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
A physical pendulum is any rigid object that is free to oscillate about some fixed axis. The period of oscillation of a physical pendulum is not necessarily the same as that of a simple pendulum.
38
Fisica Generale - Alan Giambattista, Betty McCarty Richardson
A force can be applied periodically to a damped oscillator (a forced oscillation).
When the force is applied at the natural frequency of the system, the amplitude of the oscillations will be a maximum. This condition is called resonance.
41
Fisica Generale - Alan Giambattista, Betty McCarty Richardson