#909 A block slides on the frictionless loop-the-loop track shown in the figure below. Find the minimum height \( h \) at which it can start from rest and still make it around the loop. Assume the size of the block is small compared to \( R \).**Diagram Explanation:**- The diagram shows a block positioned on an inclined plane at a height \( h \).- The inclined plane slopes down to meet a circular loop with radius \( R \).- An arrow on the block indicates the direction of motion down the slope.- The base of the slope leads into the vertical circle which the block must navigate. The circle represents the loop-the-loop.The objective is to determine the smallest height \( h \) necessary for the block to complete the loop without falling off the track. The circular loop’s dimensions indicate the requirement for centripetal force at the topmost point for successful traversal. The problem assumes that there is no friction on the surface.

Conserving energy between point of release and top of loop, mg(h-2R) = 0.5mv2 v2 = 2g(h-2R)…

A block slides on the frictionless loop-the-loop track shown in the figure below. Find the minimum height h at which it can start from rest and still make it around the loop. Assume the size of the block is small compared to R.

A block slides on the frictionless loop-the-loop track shown in the figure below. Find the minimum height h at which it can start from rest and still make it around the loop. Assume the size of the block is small compared to R.

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Question

#909

A block slides on the frictionless loop-the-loop track shown in the figure below. Find the minimum height \( h \) at which it can start from rest and still make it around the loop. Assume the size of the block is small compared to \( R \).

**Diagram Explanation:**

- The diagram shows a block positioned on an inclined plane at a height \( h \).
- The inclined plane slopes down to meet a circular loop with radius \( R \).
- An arrow on the block indicates the direction of motion down the slope.
- The base of the slope leads into the vertical circle which the block must navigate. The circle represents the loop-the-loop.

The objective is to determine the smallest height \( h \) necessary for the block to complete the loop without falling off the track. The circular loop’s dimensions indicate the requirement for centripetal force at the topmost point for successful traversal. The problem assumes that there is no friction on the surface.

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