An athlete with mass m running at speed v grabs a light rope that hangs from a ceiling of height H and swings to a maximum heigh
t of h1. In another room with a lower ceiling of height H/2, a second athlete with mass 2m running at the same speed v grabs a light rope hanging from the ceiling and swings to a maximum height of h2. How does the maximum height reached by the 2 athletes compare and why? (Pick one) a) The first athlete reaches a greater height, because the athlete swings on a longer rope; b) The second athlete reaches a greater height, because the athlete has a greater mass; c) The 2 athletes reach the same height, because the effect of the rope length offsets the effect of the athletes’ masses; d) The 2 athletes reach the same height, because the athletes run with the same speed.
d) The 2 athletes reach the same height, because the athletes run with the same speed.
Explanation:
In the whole process , kinetic energy is converted into potential energy .
1/2 m v² = mgh
v² = 2gh
h = v² / 2g
In this expression we see that height attained does not depend upon mass of the object . At the same time it also makes it clear that it depends upon velocity . As the velocity in both the cases are same , height attained by both of them will be same. Hence option d ) is correct.
