Newton's law of cooling states that the temperature of an object changes at a rate proportional to the difference between its te
mperature and that of its surroundings. If we measure temperature in degrees Celsius and time in minutes, the constant of proportionality k equals 0.4. Suppose the ambient temperature TA(t) is equal to a constant 38 degrees Celsius. Write the differential equation that describes the time evolution of the temperature T of the object. (a) dT dt = $$ Correct: Your answer is correct. 0.4(38-T) Suppose the ambient temp TA(t) = 38cos( π 30 t) degrees Celsius (time measured in minutes). Write the DE that describes the time evolution of temperature T of the object. (b) dT dt = Correct: Your answer is correct. If we measure time in hours the differential equation in part (b) changes. What is the new differential equation? Use the letter s to denote time in hours. (c) dT ds = If we measure time in hours and we also measure temperature in degrees Fahrenheit, the differential equation in part (c) changes even more. What is the new differential equation? Use the letter F to denote temperature in degrees Fahrenheit.
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Answer:
Part a)
Part b)
Part c)
Part d)
Net force on a closed loop in uniform magnetic field is always ZERO
Explanation:
As we know that force on a current carrying wire is given as
now we have
Part a)
current in side 166 cm and magnetic field is parallel
so we have
here we know that L and B is parallel to each other so
Part b)
For 68.1 cm length wire we have
here we know that
so we have
Part c)
For 151 cm length wire we have
here we know that
so we have
Part d)
Net force on a closed loop in uniform magnetic field is always ZERO