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A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What

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Question: A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What is its speed at the bottom of the incline?

Options:

  1. 10 m/s
  2. 5 m/s
  3. 20 m/s
  4. 15 m/s

Correct Answer: 10 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 * 9.81 * 5) = 10 m/s.

A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What

Practice Questions

Q1
A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What is its speed at the bottom of the incline?
  1. 10 m/s
  2. 5 m/s
  3. 20 m/s
  4. 15 m/s

Questions & Step-by-Step Solutions

A block of mass 2 kg is sliding down a frictionless incline of height 5 m. What is its speed at the bottom of the incline?
  • Step 1: Identify the mass of the block, which is 2 kg.
  • Step 2: Identify the height of the incline, which is 5 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 g is the acceleration due to gravity (approximately 9.81 m/s²).
  • Step 5: Calculate the potential energy at the top: PE = 2 kg * 9.81 m/s² * 5 m.
  • Step 6: Calculate the potential energy: PE = 2 * 9.81 * 5 = 98.1 Joules.
  • Step 7: At the bottom, all potential energy converts to kinetic energy (KE), which is given by the formula KE = 0.5 * mv².
  • Step 8: Set the potential energy equal to the kinetic energy: 98.1 Joules = 0.5 * 2 kg * v².
  • Step 9: Simplify the equation: 98.1 = 1 * v², so v² = 98.1.
  • Step 10: Take the square root of both sides to find v: v = sqrt(98.1).
  • Step 11: Calculate the speed: v ≈ 9.9 m/s, which can be rounded to 10 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 the top of the incline and kinetic energy (0.5mv²) at the bottom.
  • Motion on an Incline – Analyzing the motion of an object sliding down an incline, particularly under the influence of gravity.
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