At a horse race, all horses started from rest. As soon as the gates were open the horses started to trot. After 300s, Blacky was
1 answer:
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1) Physical principles:
a) Total mechanical energy = kinetic energy + potential energy.
b) Total mechanical energy is conserved (neglecting external forces, like drag and friction)
2) Notation:
a) Total mechanical energy: ME.
b) Kinetic energy: KE
c) Gravitational potential energy: PE
∴ ME = KE + PE = constant
3) Solution:
a) Since, ME is conserved, it is constant and would be represented in the graph by a horizontal line.
b) At start (t = 0), the ball has only KE, so KE =ME = E and PE = 0
c) As the time goes, the ball gains altitude (PE increases) and loses speed (KE decreases).
d) PE increases from 0 to a maximum value. In the graph that happens at t = 2s.
At that point, KE = 0, and PE = ME.
That is the point of highest altitude and where the speed is zero.
d) From t = 2 seg, the ball starts to lose altitude, then the ball loses PE, and gains KE.
Just before reaching the ground, at t = 4s, the ball has the same initial KE and PE as at t = 0: KE = ME and PE = 0.
The PE may be sketched on the same graph along with the KE and the ME.
The graph is attached. The red line is the ME and the blue line is the PE.
Note that at any point in the graph PE + KE = ME.
Answer:
a) 3000 Hz;
b) 30 dB;
c) 1000 times.
Explanation:
a) From the human audiogram given on the figure below the black line represents the threshold for hearing the sound at each frequency. We see that the least intensity is necessary for the frequency of about 3000 Hz.
b) Using the same audiogram we see that we would need the sound of the intensity of about 30dB.
c) The least perceptible sound at 1000 Hz must be 0dB while at 100 Hz it is 30dB. These are logarithmic quantities. To transform them to the linear quantities we use the formula
where is the hearing threshold at 1000 Hz.
Therefore we have the following
is the threshold at 1000Hz and
is the threshold at 100Hz.
By exponentiating we have
Now dividing these two equations we get
Therefore, the least perceptible sound at 100Hz is 1000 times more intense than the least perceptible sound at 1000Hz.
Note: I got these values unisng the audiogram that is attached here. The one that you have might be slightly different and might yield different answers.
