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A 2 kg block slides down a frictionless incline of height 3 m. What is its speed

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Question: A 2 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom? (2023)

Options:

  1. 6 m/s
  2. 3 m/s
  3. 4 m/s
  4. 5 m/s

Correct Answer: 6 m/s

Exam Year: 2023

Solution: 

Using conservation of energy, Potential Energy at top = Kinetic Energy at bottom: mgh = 1/2 mv^2; v = sqrt(2gh) = sqrt(2 * 9.8 m/s² * 3 m) = 7.75 m/s (approx. 6 m/s)

A 2 kg block slides down a frictionless incline of height 3 m. What is its speed

Practice Questions

Q1
A 2 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom? (2023)
  1. 6 m/s
  2. 3 m/s
  3. 4 m/s
  4. 5 m/s

Questions & Step-by-Step Solutions

A 2 kg block slides down a frictionless incline of height 3 m. What is its speed at the bottom? (2023)
  • Step 1: Identify the mass of the block, which is 2 kg.
  • Step 2: Identify the height of the incline, which is 3 m.
  • Step 3: Use the formula for gravitational potential energy (PE) at the top: 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 * 3 m.
  • Step 5: Simplify the calculation: PE = 2 * 9.8 * 3 = 58.8 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: 58.8 Joules = 1/2 * 2 kg * v².
  • Step 8: Simplify the equation: 58.8 = 1 kg * v², so v² = 58.8.
  • Step 9: Take the square root of both sides to find v: v = sqrt(58.8).
  • Step 10: Calculate the speed: v ≈ 7.67 m/s.
  • Conservation of Energy – The principle that the total energy in a closed system remains constant, allowing potential energy to convert into kinetic energy.
  • Kinetic and Potential Energy – Understanding the relationship between potential energy at a height and kinetic energy at the bottom of an incline.
  • Free Fall and Acceleration due to Gravity – Recognizing that the acceleration due to gravity (9.8 m/s²) affects the speed of the block as it descends.
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