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### Problem Statement A mass \( m \) slides down the looped track below, which is considered frictionless. If the loop has radius \( r \): (a) What is the minimum height \( h \) needed so that the mass makes it over and around the loop? (b) If the actual release height is \( 2h \), calculate the normal force exerted by the track at the bottom of the loop. (c) Calculate the normal force exerted by the track at the top of the loop. (d) Calculate the normal force exerted by the track after the block exits the loop onto the flat section. ### Diagram Explanation The diagram shows a track with a block at height \( h \) that leads into a vertical loop with radius \( R \). After the loop, the track continues in a flat horizontal section. 1. **Initial Position**: The block starts from a height \( h \) on an inclined section of the track. 2. **Loop**: The loop is circular with a clear indication of radius \( R \). 3. **Flat Section**: The track ends with a horizontal flat section after the loop.
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Transcribed Image Text:### Problem Statement A mass \( m \) slides down the looped track below, which is considered frictionless. If the loop has radius \( r \): (a) What is the minimum height \( h \) needed so that the mass makes it over and around the loop? (b) If the actual release height is \( 2h \), calculate the normal force exerted by the track at the bottom of the loop. (c) Calculate the normal force exerted by the track at the top of the loop. (d) Calculate the normal force exerted by the track after the block exits the loop onto the flat section. ### Diagram Explanation The diagram shows a track with a block at height \( h \) that leads into a vertical loop with radius \( R \). After the loop, the track continues in a flat horizontal section. 1. **Initial Position**: The block starts from a height \( h \) on an inclined section of the track. 2. **Loop**: The loop is circular with a clear indication of radius \( R \). 3. **Flat Section**: The track ends with a horizontal flat section after the loop.
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