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Question #42339
The Question
A small block of mass slides with speed along a smooth horizontal platform. The platform ends at point , where the block enters the inside of a fixed vertical circular track of radius . The center of the track is at a height above the platform, and the block moves downwards along the track after entry. The track is smooth everywhere except at , where there is a small rough patch with a coefficient of friction . The collision of the block with the track at is perfectly inelastic in the normal direction. Find the minimum value of required for the block to complete the vertical circle without losing contact with the track.
Options
- A.
- B.
- C.
- D.
Check Your Answer
Correct Answer
Step-by-Step Solution
Explanation
How the Examiner Thinks
Intuition_Breaker
Train your brain to resist "obvious" answers that are designed to deceive your intuition.
Concepts Behind This Question
Coefficient of Restitution|Vertical Circular Motion|Vector Cross-Products
Why This Question Is Tricky
Common Mistakes
This question tests the student's ability to recognize and quantify impulsive surface forces during a friction-transition phase.
The lethal trap lies in assuming that friction is non-impulsive or ignoring it entirely during the collision.
Students often correctly resolve the velocity to find the tangential component but fail to realize that the destruction of the normal velocity component generates an impulsive normal force.
This, in turn, creates an impulsive frictional force that causes a discontinuous drop in the tangential velocity.
Furthermore, students must correctly apply the loop-completion constraint ( at the top) and calculate the correct height difference from the entry point.
Quick Facts About This Question
Question Information
| Subject | Physics |
| Chapter | Work, Energy, and Power - Class 11 Part 1 |
| Concept | Coefficient of Restitution |
| Difficulty | 8 |
| Cognitive Load | 7 |
| Target Solve Time | 160 sec |
| Access | Free |