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A pendulum of length 2 m swings from a height of 1 m. What is the speed at the l

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Question: A pendulum of length 2 m swings from a height of 1 m. What is the speed at the lowest point of the swing? (g = 9.8 m/s²)

Options:

  1. 4.4 m/s
  2. 3.1 m/s
  3. 2.8 m/s
  4. 5.0 m/s

Correct Answer: 4.4 m/s

Solution: 

Using conservation of energy, potential energy at the top = kinetic energy at the bottom. mgh = 0.5mv². Solving gives v = sqrt(2gh) = sqrt(2 * 9.8 * 1) = 4.4 m/s.

A pendulum of length 2 m swings from a height of 1 m. What is the speed at the l

Practice Questions

Q1
A pendulum of length 2 m swings from a height of 1 m. What is the speed at the lowest point of the swing? (g = 9.8 m/s²)
  1. 4.4 m/s
  2. 3.1 m/s
  3. 2.8 m/s
  4. 5.0 m/s

Questions & Step-by-Step Solutions

A pendulum of length 2 m swings from a height of 1 m. What is the speed at the lowest point of the swing? (g = 9.8 m/s²)
  • Step 1: Identify the height from which the pendulum swings. In this case, it is 1 meter.
  • Step 2: Identify the length of the pendulum, which is 2 meters. This is not directly needed for the calculation but helps understand the setup.
  • Step 3: Use the formula for gravitational potential energy (PE) at the height: PE = mgh, where m is mass, g is the acceleration due to gravity (9.8 m/s²), and h is the height (1 m).
  • Step 4: At the lowest point of the swing, all potential energy is converted into kinetic energy (KE). The formula for kinetic energy is KE = 0.5mv².
  • Step 5: Set the potential energy equal to the kinetic energy: mgh = 0.5mv². The mass (m) cancels out from both sides of the equation.
  • Step 6: Rearrange the equation to solve for v (speed): gh = 0.5v².
  • Step 7: Multiply both sides by 2 to eliminate the 0.5: 2gh = v².
  • Step 8: Take the square root of both sides to find v: v = sqrt(2gh).
  • Step 9: Substitute the values for g (9.8 m/s²) and h (1 m) into the equation: v = sqrt(2 * 9.8 * 1).
  • Step 10: Calculate the value: v = sqrt(19.6) which is approximately 4.4 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.
  • Potential Energy – The energy stored in an object due to its height above the ground, calculated as mgh.
  • Kinetic Energy – The energy of an object in motion, calculated as 0.5mv².
  • Pendulum Motion – The motion of a pendulum involves converting potential energy at its highest point to kinetic energy at its lowest point.
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