A baking dish is removed from a hot oven and placed on a cooling rack. As the dish cools down to 35 C from 175 C, its net radian
t power decreases to 12.0 W. What was the net radiant power of the baking dish when it was first removed from the oven? Assume that the temperature in the kitchen remains at 22 C as the dish cools down.
1 answer:
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Answer:
The rotational frequency must be 2073.56 rpm
Explanation:
Notice that we need to obtain a rotational frequency in "rpm" (revolutions per minute), so we better start by converting all the given information into the appropriate units:
The magnitude of the velocity for the pitch is given in miles per hour, while the diameter of the machine's wheels is given in cm. Let's reduce all units of length into meters(using the metric system), and the units of time into minutes.
Conversion of the 85 mph speed into meters per minute:
Recall that 1 mile equals 1609.34 meters, and that 1 hour equals 60 minutes, so we write:
which can be rounded to approximately 2280 m/min.
We also convert the 35 cm diameter into meters:
diameter = 0.35 m
Now we use the equation that relates angular velocity (w) and the radius (R) of the circular movement, with tangential velocity (), in order to obtain the angular velocity of the wheel:
but recall that this angular velocity is given in radians per unit of time. So first find the radius of the wheel (half its diameter). R = 0.175 m
So we have:
And now, recalling that radians equal one revolution, we convert the angular velocity ot revolutions per minute by dividing the "w" we found by
:
rotational frequency =
(a) Since the ambulance and the car are moving one relative to each other, we have to use the general formula of the Doppler effect, which gives us the shift of the frequency of the siren as heard by an observer in the car:
where
f' is the apparent frequency as heard by the observer in the car
v is the velocity of the wave
is the velocity of the observer (positive if it is moving towards the source, negative if it is moving away)
is the velocity of the source (positive if the source is moving away from the observer, negative if is is moving towards it)
f is the real frequency of the sound
In the first part of the problem:
(speed of the sound wave)
(the car is moving away from the ambulance)
(the ambulance is moving towards the car)
(original frequency of the sound)
If we plug the numbers into the formula, we find
b) This time, the ambulance passes the car, so the ambulance is now moving away from the car; this means that must be positive:
Moreover, the car is now moving towards the ambulance, so we should reverse also the sign of:
All the other data do not change, so if we use the same formula as before, we find
where
f' is the apparent frequency as heard by the observer in the car
v is the velocity of the wave
f is the real frequency of the sound
In the first part of the problem:
If we plug the numbers into the formula, we find
b) This time, the ambulance passes the car, so the ambulance is now moving away from the car; this means that
Moreover, the car is now moving towards the ambulance, so we should reverse also the sign of
All the other data do not change, so if we use the same formula as before, we find