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A solid cone rolls down an incline. If its height is h, what is the relationship

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Question: A solid cone rolls down an incline. If its height is h, what is the relationship between its potential energy and kinetic energy at the bottom?

Options:

  1. PE = KE
  2. PE = 2KE
  3. PE = 3KE
  4. PE = 4KE

Correct Answer: PE = 2KE

Solution: 

For a solid cone rolling down an incline, the potential energy at height h is converted into translational and rotational kinetic energy, leading to PE = 2KE.

A solid cone rolls down an incline. If its height is h, what is the relationship

Practice Questions

Q1
A solid cone rolls down an incline. If its height is h, what is the relationship between its potential energy and kinetic energy at the bottom?
  1. PE = KE
  2. PE = 2KE
  3. PE = 3KE
  4. PE = 4KE

Questions & Step-by-Step Solutions

A solid cone rolls down an incline. If its height is h, what is the relationship between its potential energy and kinetic energy at the bottom?
  • Step 1: Understand that potential energy (PE) is the energy an object has due to its height. For a solid cone at height h, the potential energy is given by PE = mgh, where m is mass and g is the acceleration due to gravity.
  • Step 2: When the cone rolls down the incline, it loses potential energy and gains kinetic energy. Kinetic energy (KE) can be divided into two types: translational kinetic energy (due to its movement) and rotational kinetic energy (due to its spinning).
  • Step 3: The total kinetic energy at the bottom of the incline is the sum of translational kinetic energy (KE_trans) and rotational kinetic energy (KE_rot).
  • Step 4: For a solid cone, the relationship between potential energy and kinetic energy at the bottom of the incline is given by the equation PE = KE_trans + KE_rot.
  • Step 5: It can be shown that for a solid cone, the rotational kinetic energy is half of the translational kinetic energy, leading to the relationship PE = 2KE, where KE is the total kinetic energy.
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another.
  • Potential Energy – The energy stored in an object due to its height above the ground, calculated as PE = mgh.
  • Kinetic Energy – The energy of an object in motion, which includes both translational and rotational components for rolling objects.
  • Rolling Motion – The combination of translational and rotational motion, where the total kinetic energy is the sum of both forms.
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