example 5 Richter Scale
Chapter 5.2
Because the intensities of earthquakes are so large, the Richter scale was developed toprovide a “scaled down” measuring system that permits earthquakes to be more easilymeasured and compared. The Richter scale gives the magnitude R of an earthquakeusing the formula
where I is the intensity of the earthquake and I0 is a certain minimum intensity used forcomparison.
0
logI
RI
2009 PBLPathways
2009 PBLPathways
Because the intensities of earthquakes are so large, the Richter scale was developed toprovide a “scaled down” measuring system that permits earthquakes to be more easilymeasured and compared. The Richter scale gives the magnitude R of an earthquakeusing the formula
where I is the intensity of the earthquake and I0 is a certain minimum intensity used forcomparison.
0
logI
RI
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Micro Less than 2.0 Microearthquakes, not felt
Very minor 2.0–2.9 Generally not felt, but recorded
Minor 3.0–3.9 Often felt, but rarely causes damage
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
Moderate 5.0–5.9 Can cause damage to poorly constructed buildings over small regions
Strong 6.0–6.9 Can be destructive in areas up to about 100 miles across in populated areas
Major 7.0–7.9 Can cause serious damage over larger areas
Great 8.0–8.9 Can cause serious damage in areas several hundred miles across
Rarely, great 9.0–9.9 Devastating in areas several thousand miles across
Meteoric 10+ Never recorded
The following table describes the typical effects of earthquakes of various magnitudesnear the epicenter.
2009 PBLPathways
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
010kI I
2009 PBLPathways
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
010,000I I
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
010,000I I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
010,000I I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
010,000I I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
010,000I I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
Description Richter Magnitudes Earthquake Effects
Light 4.0–4.9 Noticeable shaking of indoor items, rattling noises. Significant damage unlikely
0
0
0
log
10,000log
log 10,000
4
IR
I
I
I
a. If an earthquake has an intensity of 10,000 times I0 , what is the magnitude of the earthquake? Describe the effects of this earthquake.
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
b. Show that if the Richter scale reading of an earthquake is k, the intensity of the earthquake is .010kI I
0
logI
kI
Convert to
exponential form 0
00 0
0
10
10
10
k
k
k
II
I
I
I
I
I
I
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
2009 PBLPathways
c. An earthquake that measured 9.0 on the Richter scale occurred in the Indian Ocean in December 2004, causing a devastating tsunami that killed thousands of people. Express the intensity of this earthquake in terms of I0.
d. If an earthquake measures 7.0 on the Richter scale, give the intensity of this earthquake in terms of I0. How much more is the intensity of the earthquake in part (c) than the one with Richter scale measurement of 7.0?
9.00 010 1,000,000,000I I I
9.0 9.020
7.0 7.00
10 1010 100
10 10
I
I
7.0010I I
9.0010I IRichter scale 9.0:
Richter scale 7.0:
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