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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?

Options:

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

Correct Answer: 10 m/s

Solution: 

Using conservation of energy, potential energy at the top (mgh) converts to kinetic energy at the bottom (1/2 mv²). Thus, v = sqrt(2gh) = sqrt(2 * 9.8 * 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?
  1. 5 m/s
  2. 10 m/s
  3. 15 m/s
  4. 20 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?
  • 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: Use the formula for potential energy (PE) at the top of the incline: PE = mgh, where g is the acceleration due to gravity (approximately 9.8 m/s²).
  • Step 4: Calculate the potential energy at the top: PE = 2 kg * 9.8 m/s² * 5 m.
  • Step 5: Calculate PE = 2 * 9.8 * 5 = 98 joules.
  • Step 6: At the bottom of the incline, all potential energy converts to kinetic energy (KE). The formula for kinetic energy is KE = 1/2 mv².
  • Step 7: Set the potential energy equal to the kinetic energy: 98 joules = 1/2 * 2 kg * v².
  • Step 8: Simplify the equation: 98 = 1 * v², so v² = 98.
  • Step 9: Take the square root of both sides to find v: v = sqrt(98).
  • Step 10: Calculate v: v ≈ 9.9 m/s, which we can round to approximately 10 m/s.
  • Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another.
  • Kinetic and Potential Energy – Understanding the relationship between potential energy (mgh) at the top of the incline and kinetic energy (1/2 mv²) at the bottom.
  • Motion on Inclines – Analyzing the motion of objects on inclined planes, particularly in the absence of friction.
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