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4. The radioactive isotope Cobalt 60 has a half-life of 5.27 years. In that period of time half of the Cobalt 60 will decay into Nickel 60 which is not radioactive. a. Determine the exponential equation of the form y = Ae-kt which describes the quantity of cobalt 60 present if it is 20 kg at t=0. b. Determine the time at which only 1 microgram (1 µg) remains.

4. The radioactive isotope Cobalt 60 has a half-life of 5.27 years. In that period of time half of the Cobalt 60 will decay into Nickel 60 which is not radioactive. a. Determine the exponential equation of the form y = Ae-kt which describes the quantity of cobalt 60 present if it is 20 kg at t=0. b. Determine the time at which only 1 microgram (1 µg) remains.

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d. What is this same ratio represented as dB? e. In the case of a radar signal, the power will diminish by - d? on the way to the object you 1 are searching for, and the reflection will diminish by another on the way back. So in d2 this case, Preceived = Ptransmitted · k·. Our now upgraded radar is transmitting d4 96dBm, and can still successfully receive as little as -125 dBm. If the target is 1 km away, the received power would be 0 dBm. What is the value of k? f. How many times farther away can the target be for the radar to still be able to see it? 4. The radioactive isotope Cobalt 60 has a half-life of 5.27 years. In that period of time half of the Cobalt 60 will decay into Nickel 60 which is not radioactive. Determine the exponential equation of the form y = Ae-kt which describes the а. quantity of cobalt 60 present if it is 20 kg at t=0. b. Determine the time at which only 1 microgram (1 µg) remains. 5. When power is applied to a microprocessor, we want the software to start cleanly. To do this, we put a signal on a Reset pin that will not reach 2.5 V until the Voltage to the processor has been at 5V for a period of time. This signal is created by a circuit consisting of a resistor R from the power pin to the reset pin and a capacitor C from the reset pin to the circuit ground. Assuming the power transition from 0 to 5 V happens cleanly at t=0, the signal on the reset pin will have the form Vpin = 5V · (1 - e -(Rct)) a. If the time (t) before the reset pin (V,in) reaches 2.5 V needs to be at least 2 ms, and C is 20µF, what would the value for R have to be? b. If the threshold is increased to 3.0 V, but the same R and C values are used, how much longer will that make the time t ?
Transcribed Image Text:d. What is this same ratio represented as dB? e. In the case of a radar signal, the power will diminish by - d? on the way to the object you 1 are searching for, and the reflection will diminish by another on the way back. So in d2 this case, Preceived = Ptransmitted · k·. Our now upgraded radar is transmitting d4 96dBm, and can still successfully receive as little as -125 dBm. If the target is 1 km away, the received power would be 0 dBm. What is the value of k? f. How many times farther away can the target be for the radar to still be able to see it? 4. The radioactive isotope Cobalt 60 has a half-life of 5.27 years. In that period of time half of the Cobalt 60 will decay into Nickel 60 which is not radioactive. Determine the exponential equation of the form y = Ae-kt which describes the а. quantity of cobalt 60 present if it is 20 kg at t=0. b. Determine the time at which only 1 microgram (1 µg) remains. 5. When power is applied to a microprocessor, we want the software to start cleanly. To do this, we put a signal on a Reset pin that will not reach 2.5 V until the Voltage to the processor has been at 5V for a period of time. This signal is created by a circuit consisting of a resistor R from the power pin to the reset pin and a capacitor C from the reset pin to the circuit ground. Assuming the power transition from 0 to 5 V happens cleanly at t=0, the signal on the reset pin will have the form Vpin = 5V · (1 - e -(Rct)) a. If the time (t) before the reset pin (V,in) reaches 2.5 V needs to be at least 2 ms, and C is 20µF, what would the value for R have to be? b. If the threshold is increased to 3.0 V, but the same R and C values are used, how much longer will that make the time t ?
1. On a communication link in the open air away from the ground and other objects the signal power at the receiving radio will typically obey an inverse square law relative to the distance between the transmitted and receiver. So Preceived = Ptransmitted ' k2 If Prransmitted = 0.35 mW , k = 1.8 m² , and the distance d = 256 m , what is the а. received power Preceived ? b. What is this received power in dBW (deciBels relative to 1 Watt)? If both the transmitter and the receiver are close to the ground, the power loss can be с. much higher. If the loss is proportional to d-3.5 instead of , but the other values are d2 ' the same as in part a, what is the new received power Preceived ? d. What is this new received power in dBW? 2. Earthquakes are measured with a logarithmic Moment Magnitude scale. This scale takes a seismic moment value and creates a Moment Magnitude roughly comparable to earlier Richter scale measurements. The seismic moment in turn is calculated from the area of the fault that breaks free, the distance the fault is displaced, and the rigidity of the material adjacent to the fault. If the seismic moment is M. , the Moment Magnitude is calculated as Mw M. 10 -6. Nm, а. Not very long ago (Sept. 3, 2016) we experienced the strongest earthquake yet in Oklahoma, with an epicenter near Pawnee, determined to have a Moment Magnitude Mw of 5.8. What was the corresponding seismic moment M,? b. If the seismic moment of a subsequent earthquake was 2·1015 (as occurred on Aug. 3, 2017, about 6 miles from here), what would the Moment Magnitude of this earthquake be? C. On March 27, 1964 an earthquake occurred in southern Alaska. Although few instruments we available in the area at that time to record it accurately, subsequent analysis of the displacements and materials in the area produced a calculated M,of 9.2. What was the Seismic Moment M, of this earthquake? d. Plot the moment magnitude for these three events, from smaller to larger. What would happen if you instead plotted the seismic moments of the 3? 3. We use electromagnetic signals over a very wide range in power. In order to represent them more conveniently we often refer to the power of such signals in dBm , which stands for decibels referenced to a milliWatt. Consequently, if the power in Watts is Pw , then the equivalent power in dBm is PaBm = 10 log10(Pw · 1000) = 10 log10(Pw) + 30. If a radar system transmits an effective power of 2MW (2 million Watts), what is this signal power in dBm? а. b. If the radar can detect signals of -125 dBm what is the power of those signals in Watts? C. What is the ratio of the power transmitted to power received as a number?
Transcribed Image Text:1. On a communication link in the open air away from the ground and other objects the signal power at the receiving radio will typically obey an inverse square law relative to the distance between the transmitted and receiver. So Preceived = Ptransmitted ' k2 If Prransmitted = 0.35 mW , k = 1.8 m² , and the distance d = 256 m , what is the а. received power Preceived ? b. What is this received power in dBW (deciBels relative to 1 Watt)? If both the transmitter and the receiver are close to the ground, the power loss can be с. much higher. If the loss is proportional to d-3.5 instead of , but the other values are d2 ' the same as in part a, what is the new received power Preceived ? d. What is this new received power in dBW? 2. Earthquakes are measured with a logarithmic Moment Magnitude scale. This scale takes a seismic moment value and creates a Moment Magnitude roughly comparable to earlier Richter scale measurements. The seismic moment in turn is calculated from the area of the fault that breaks free, the distance the fault is displaced, and the rigidity of the material adjacent to the fault. If the seismic moment is M. , the Moment Magnitude is calculated as Mw M. 10 -6. Nm, а. Not very long ago (Sept. 3, 2016) we experienced the strongest earthquake yet in Oklahoma, with an epicenter near Pawnee, determined to have a Moment Magnitude Mw of 5.8. What was the corresponding seismic moment M,? b. If the seismic moment of a subsequent earthquake was 2·1015 (as occurred on Aug. 3, 2017, about 6 miles from here), what would the Moment Magnitude of this earthquake be? C. On March 27, 1964 an earthquake occurred in southern Alaska. Although few instruments we available in the area at that time to record it accurately, subsequent analysis of the displacements and materials in the area produced a calculated M,of 9.2. What was the Seismic Moment M, of this earthquake? d. Plot the moment magnitude for these three events, from smaller to larger. What would happen if you instead plotted the seismic moments of the 3? 3. We use electromagnetic signals over a very wide range in power. In order to represent them more conveniently we often refer to the power of such signals in dBm , which stands for decibels referenced to a milliWatt. Consequently, if the power in Watts is Pw , then the equivalent power in dBm is PaBm = 10 log10(Pw · 1000) = 10 log10(Pw) + 30. If a radar system transmits an effective power of 2MW (2 million Watts), what is this signal power in dBm? а. b. If the radar can detect signals of -125 dBm what is the power of those signals in Watts? C. What is the ratio of the power transmitted to power received as a number?
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