Sketch two cycles for the motion above the ground of a point on a hamster wheel. The wheel rotates every 6 seconds. The highest it reaches is 27 cm above the ground. The diameter of the wheel is 25 cm.
see the graph at
http://www.wolframalpha.com/input/?i=plot+y%3D29%2F2+-+25%2F2+cos(pi%2F3+t),+y%3D2,y%3D27+for+0%3C%3Dt%3C%3D12
use what you know about shifts, periods, and amplitudes to arrive at it.
To sketch two cycles of the motion of a point on a hamster wheel, we need to understand how the wheel rotates and how the point moves.
First, let's determine the circumference of the wheel. The diameter of the wheel is given as 25 cm, so we can calculate the circumference using the formula:
Circumference = π * Diameter
C = π * 25 cm
C ≈ 78.54 cm
This means that for every full rotation of the wheel, the point on the wheel travels a distance of approximately 78.54 cm.
Next, let's determine how long it takes for the wheel to complete one full rotation. It's given that the wheel rotates every 6 seconds. Therefore, the time period for one rotation is 6 seconds.
Now, let's plot the motion of the point on the wheel over two cycles.
In one cycle, the point starts at its lowest position (point A), and as the wheel rotates, the point gradually moves upward, reaching its highest position (point B) at 27 cm above the ground. Then, the point moves back down to its lowest position (point C) as the wheel completes one full rotation. Finally, the point moves back up to point A.
For the second cycle, the point will follow the same motion pattern. It starts at point A, rises to point B, then moves back down to point C, and returns to point A.
To sketch the cycles, draw a horizontal line to represent the ground level. Mark points A, B, and C on this horizontal line. For each cycle, draw a curve connecting the points A, B, and C, representing the motion of the point on the hamster wheel.
Keep in mind that the distances between points A and B, and points B and C will be different from the distances between the ground and point A (lowest position) and ground and point B (highest position). The distances mentioned are given to help you understand the motion but are not directly related to the distances traveled by the point on the wheel.