You see an advertisement for a new free fall ride at an amusement park. The ad says the ride is 50 meters tall and reaches a speed of 28 m/s at the bottom. How efficient is the ride?
*Hint: You can use any mass you wish because it cancels out.*
Answer (2)
Explanation :
It is given that the ad says the ride is 50 meters tall and reaches a speed of 28m/sec at the bottom.
The efficiency is defined as the ratio of the output energy and the input energy.
In this case, the output energy is kinetic energy and the input is potential energy.
Output energy, E k = 2 1 × m v 2
Input energy, E p = m g h
Efficiency becomes :
E = 2 g h 1 × v 2
E = 2 × 9.8 m / s 2 × 50 m 1 × ( 28 m / s ) 2
E = 0.8
or
E = 80%
The ride is 80% efficient.
The ride's efficiency is calculated to be 80%, indicating that 80% of the gravitational potential energy at the top converts to kinetic energy at the bottom. This is derived by comparing the kinetic energy at the bottom to the potential energy at the top, accounting for the height of 50 meters and the speed of 28 m/s. The mass cancels out in the calculations, allowing us to focus on the energy values directly.
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