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A cylinder rolls down a hill. If the height of the hill is h, what is the speed

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Question: A cylinder rolls down a hill. If the height of the hill is h, what is the speed of the cylinder at the bottom assuming no energy losses?

Options:

  1. √(2gh)
  2. √(3gh)
  3. √(gh)
  4. √(4gh)

Correct Answer: √(2gh)

Solution: 

Using conservation of energy, potential energy at height h converts to kinetic energy at the bottom. The speed is √(2gh).

A cylinder rolls down a hill. If the height of the hill is h, what is the speed

Practice Questions

Q1
A cylinder rolls down a hill. If the height of the hill is h, what is the speed of the cylinder at the bottom assuming no energy losses?
  1. √(2gh)
  2. √(3gh)
  3. √(gh)
  4. √(4gh)

Questions & Step-by-Step Solutions

A cylinder rolls down a hill. If the height of the hill is h, what is the speed of the cylinder at the bottom assuming no energy losses?
  • Step 1: Understand that the cylinder starts at a height 'h' on the hill.
  • Step 2: Recognize that at the top of the hill, the cylinder has potential energy due to its height.
  • Step 3: Know that potential energy (PE) can be calculated using the formula PE = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height.
  • Step 4: As the cylinder rolls down the hill, this potential energy converts into kinetic energy (KE) at the bottom.
  • Step 5: The formula for kinetic energy is KE = 0.5 * m * v^2, where 'v' is the speed of the cylinder.
  • Step 6: Since there are no energy losses, the potential energy at the top equals the kinetic energy at the bottom: mgh = 0.5 * m * v^2.
  • Step 7: Cancel the mass 'm' from both sides of the equation (since it is the same on both sides).
  • Step 8: Rearrange the equation to solve for 'v': 2gh = v^2.
  • Step 9: Take the square root of both sides to find the speed: v = √(2gh).
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another.
  • Potential Energy – The energy possessed by an object due to its position in a gravitational field, calculated as mgh.
  • Kinetic Energy – The energy of an object in motion, calculated as (1/2)mv².
  • Rolling Motion – The motion of a body that rolls without slipping, which involves both translational and rotational kinetic energy.
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