In the figure, a horizontally moving block can take three frictionless routes, d

Question

In the figure, a horizontally moving block can take three frictionless routes, differing only in elevation, to reach the dashed finish line. In the following questions, you will need to rank the routes. If multiple routes rank equally, use the same rank for each, then exclude the intermediate ranking (i.e. if objects A, B, and C must be ranked, and A and B must both be ranked first, the ranking would be A:1, B:1, C:3). If all routes rank equally, rank each as '1'. Rank the routes according to the speed of the block at the finish line, greatest first. Route 1 Route 2 Route 3 Greatest Second greatest Third greatest Rank the routes according to the speed of the block at the finish line, greatest first. Route 1 Route 2 Route 3 Greatest Second greatest Third greatest

Explanation / Answer

Solution: As the paths are frictionless, conservation of energy will be obeyed for each path. For path 1, kinetic energy will decrease for increase in potential energy; so v will decrease. For path 2, velocity will remain same. For path 3, kinetic energy will increase for decrease in potential energy; so v will increase. Therefore, the ranking of routes according to speed (greatest first) will be: 1. Route 3, 2. Route 2 and 3. Route 1.

As v is least for route 1, travel time will be highest for this case. Therefore, the ranking of routes according to travel time (greatest first) will be: 1. Route 1, 2. Route 2 and 3. Route 3.

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