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A block of mass 2 kg is sliding down a frictionless incline of height 10 m. What

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Question: A block of mass 2 kg is sliding down a frictionless incline of height 10 m. What is its speed at the bottom?

Options:

  1. 10 m/s
  2. 14 m/s
  3. 20 m/s
  4. 25 m/s

Correct Answer: 14 m/s

Solution: 

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Thus, v = sqrt(2gh) = sqrt(2 * 9.8 * 10) = 14 m/s.

A block of mass 2 kg is sliding down a frictionless incline of height 10 m. What

Practice Questions

Q1
A block of mass 2 kg is sliding down a frictionless incline of height 10 m. What is its speed at the bottom?
  1. 10 m/s
  2. 14 m/s
  3. 20 m/s
  4. 25 m/s

Questions & Step-by-Step Solutions

A block of mass 2 kg is sliding down a frictionless incline of height 10 m. What is its speed at the bottom?
  • Step 1: Identify the mass of the block, which is 2 kg.
  • Step 2: Identify the height of the incline, which is 10 m.
  • Step 3: Understand that the block starts with potential energy at the top and converts it to kinetic energy at the bottom.
  • Step 4: Use the formula for potential energy (PE) at the top: PE = mgh, where m is mass, g is acceleration due to gravity (approximately 9.8 m/s²), and h is height.
  • Step 5: Calculate the potential energy at the top: PE = 2 kg * 9.8 m/s² * 10 m = 196 Joules.
  • Step 6: At the bottom, all potential energy converts to kinetic energy (KE). The formula for kinetic energy is KE = 0.5 * mv².
  • Step 7: Set the potential energy equal to the kinetic energy: 196 Joules = 0.5 * 2 kg * v².
  • Step 8: Simplify the equation: 196 = 1 * v², so v² = 196.
  • Step 9: Take the square root of both sides to find v: v = sqrt(196) = 14 m/s.
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another, in this case from potential energy to kinetic energy.
  • Kinetic and Potential Energy – Understanding the relationship between potential energy (mgh) at a height and kinetic energy (0.5mv²) at the bottom of the incline.
  • Frictionless Surfaces – Recognizing that the absence of friction simplifies the energy transformation process.
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