Electrostats + Mechanics = Fun

Classical Mechanics Level 5

You took a Hollow spherical ball and gave it an angular velocity \( \omega = 10\text{ rad/sec} \) (clockwise) and dropped it from a height \( h = 45.5\text{ m}\). Above the rough horizontal ground ,In a region of uniform Electric field , \( E = 6 × {10}^{6}\text{ N/C} \) directed in the horizontal direction (Right).

We observed that after it's collision with the ground it goes to a maximum height of \(2.3\text{ m}\).

Find the Range of the projectile travelled by the ball's centre of mass in between first and second collision.

Details and Assumptions:

  • The ball has a mass \( M = 2\text{ kg} \) and is uniformly charged \(( q = 3\mu C )\). Radius of ball \( R = 0.5 \text{ m}\)

  • The height measured is of centre of mass of ball from the ground.

  • The ball remained in contact with the ground for \( t = {10}^{-6} \text{ sec}\).

  • Coefficient of friction \( \mu = \dfrac{1}{3} \), take \( g = 10\text{ m/s}^2 \).

This is a part of my set Aniket's Mechanics Challenges


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