Concept explainers
The three cups shown below are rolled on a level surface. Rank the cups by the amount they depart from a straight-line path (most curved to least curved).
To rank: The cups on the basis of the amount they depart from a straight-line path.
Answer to Problem 18A
The rank of the cups by the amount they depart from a straight-line path is
Explanation of Solution
Given:
The given figure is shown below.
Formula used:
Linear speed varies with the distance from the axis of rotation. The expression for the linear or tangential speed is,
Here,
Tangential speed depends on rotational speed and the distance from the axis of rotation.
Calculation:
The linear speed is directly proportional to the radius of its circular path.
For case A:
Both the ends of cup A have the same radius. So the ends of cup A are moving with the equal speed.
Hence, the cup A is moving along the flat surface.
For case B:
The radius of the top end of cup B is greater than the radius of the bottom end of cup B. So the speed at the top end of cup B is more when compared to the bottom end of cup B.
Hence, the cup B is moving along the flat surface and it makes a most circular path.
For case C:
The radius of the top end of cup C is greater than the radius of the bottom end of cup B and it is nearer to the top radius. So the speed at the top end of cup B is nearer when compared to the bottom end of cup C.
Hence, the cup C is moving along the flat surface and it makes a least circular path compared to cup B.
By comparing the circular path is
Conclusion:
Thus, the rank of the cups by the amount they depart from a straight-line path is
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