Potential Energy & Equilibrium: Practice Problem & Solution
A particle is released from height \(S\) from the surface of the Earth. At a certain height its kinetic energy is three times its potential energy. The height from the surface of earth and the speed of the particle at that instant are respectively
Solution Explained:
To solve this problem, we apply the core principles of Potential Energy & Equilibrium. Understanding the underlying formula is key to arriving at the correct answer below:
Total mechanical energy is \(E = mgS\). At height \(h\), \(KE = 3 PE⇒ E = KE + PE = 4 PE ⇒ mgS = 4mgh ⇒ h = S/4\). Also, \(\frac{1}{2}mv^2 = 3mg(S/4) ⇒ v = \sqrt{\frac{3gS}{2}}\).
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