does NOT. How on earth can this be? What is different about the dynamics of a hoop that rolls without slipping in this configuration and the skater?
does NOT. How on earth can this be? What is different about the dynamics of a hoop that rolls without slipping in this configuration and the skater?
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Question
Transcribed Image Text:**Rolling Down the Loop-the-Loop: Exploring Dynamics**
In the figure, a hoop rolls without slipping down an incline starting from rest at a height "h." The loop-the-loop is at the bottom, with a negligible offset in and out of the page. The loop's height is defined as 2R, where 2R = 4.0 meters. The starting height "h" is 5.5 meters.
Interestingly, these figures prevent the hoop from making it all the way to the top of the loop-the-loop without falling off. The hoop crashes!
Conversely, a skater starting from the same height "h" successfully navigates the loop-the-loop. The skater, despite being less aerodynamic, maintains sufficient speed to complete the loop at all times without falling off. How can this difference in dynamics between a hoop and a skater be explained?
**Diagram Explanation:**
- The diagram shows a hoop at the top of an incline, marked with height "h."
- The loop-the-loop is represented by a circle with radius "R."
- The top of the loop is labeled "TOP OF LOOP."
- An arrow from "h" to the loop depicts the direction of motion as the hoop rolls down.
Expert Solution
Step 1
For the skater all the potential energy of the skater changes into kinetic energy if we neglect friction and drag because only linear motion is involved.
for the hoop as it starts to roll and come down the incline its potential energy gets converted to linear kinetic energy and rotational kinetic energy.
thus some of its potential energy gets converted to rotational kinetic energy and and its linear kinetic energy is less than the skater and that is is why it have less speed than skater when it starts climbing loop the loop.
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