A small creatures moves with constant speed in a small vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a simple harmonic motion?
A small creatures moves with constant speed in a small vertical circle on a bright day. Does its shadow formed by the sun on a horizontal plane move in a simple harmonic motion?
The correct option is B yes, at any time of the day
Well! When the sun is exactly above the vertical circle, the shadow is formed and it does SHM very much as we know from the example
in the video linking SHM to circular motion. Question here actually is "will the shadow's motion be a SHM when the sun is at some angle (say θ) ?”
Let's explore that
Let's say that the sun light from the sun makes an angle θ with the horizontal as you can see is the diagram. Since the creature moves with constant speed, the time it takes to move from A to B is the same it takes to move from B to C. Also a little geometry shows us that AB = BC. The time taken to move from C to D and then again from D to A is again same. The time period of the SHM of the shadow is castant.
Now let's check for it's acceleration at some point P after a time 't' has elapsed.
The horizontal component of acceleration at P is aCh
aCh=a sin(ω t+π2−θ)
which is an acceleration relation for SHM.
yes, at any time of the day
Well! When the sun is exactly above the vertical circle, the shadow is formed and it does SHM very much as we know from the example
in the video linking SHM to circular motion. Question here actually is "will the shadow's motion be a SHM when the sun is at some angle (say θ) ?”
Let's explore that
Let's say that the sun light from the sun makes an angle θ with the horizontal as you can see is the diagram. Since the creature moves with constant speed, the time it takes to move from A to B is the same it takes to move from B to C. Also a little geometry shows us that AB = BC. The time taken to move from C to D and then again from D to A is again same. The time period of the SHM of the shadow is castant.
Now let's check for it's acceleration at some point P after a time 't' has elapsed.
The horizontal component of acceleration at P is aCh
aCh=a sin(ω t+π2−θ)
which is an acceleration relation for SHM.
