a yo-yo is swung in a vertical circle in such a way that its total energy KE+ Pe is constant. At what point in the circle is the speed a maximum? minimum? why?
To determine the point in the circle where the speed of the yo-yo is maximum or minimum, we need to understand the concepts of kinetic energy (KE) and potential energy (PE) in a vertical circle.
In a vertical circle, the total mechanical energy is the sum of kinetic energy (KE) and potential energy (PE) and it remains constant throughout the motion.
At the highest point in the circle (top of the swing), the kinetic energy will be at its minimum, and the potential energy will be at its maximum. This is because the yo-yo is at its highest point, and as it moves downward, its potential energy decreases while its kinetic energy increases.
Conversely, at the lowest point in the circle (bottom of the swing), the kinetic energy will be at its maximum, and the potential energy will be at its minimum. This is because the yo-yo is at its lowest point, and as it moves upward, its kinetic energy decreases while its potential energy increases.
Therefore, the speed of the yo-yo will be maximum at the lowest point in the circle (bottom of the swing) and minimum at the highest point (top of the swing).
To understand why this happens, we can apply the principle of energy conservation. As the yo-yo moves in a vertical circle, the total energy (KE + PE) remains constant because there is no external energy input or loss. The energy is merely converting between kinetic and potential energy forms throughout the motion.
The speed depends on the kinetic energy, and at the bottom of the swing, where the yo-yo is closer to the ground, the potential energy is at a minimum and the kinetic energy is maximum. This results in a higher speed.
At the top of the swing, where the yo-yo is farthest from the ground, the potential energy is at a maximum, and the kinetic energy (and thus speed) is at a minimum.
In summary, the yo-yo's speed is maximum at the lowest point in the circle (bottom of the swing) where potential energy is minimum, and it is minimum at the highest point (top of the swing) where potential energy is maximum.