A pendulum swings from a height of 2 m. What is the speed at the lowest point of

A pendulum swings from a height of 2 m. What is the speed at the lowest point of the swing?

A pendulum swings from a height of 2 m. What is the speed at the lowest point of the swing?

Step 1: Understand that the pendulum swings from a height of 2 meters.
Step 2: Recognize that at the highest point, the pendulum has potential energy and at the lowest point, it has kinetic energy.
Step 3: Use the formula for potential energy (PE) at the top: PE = mgh, where m is mass, g is gravity (9.8 m/s²), and h is height (2 m).
Step 4: At the lowest point, all potential energy converts to kinetic energy (KE), which is given by the formula KE = 0.5mv².
Step 5: Set the potential energy equal to the kinetic energy: mgh = 0.5mv².
Step 6: Notice that mass (m) cancels out from both sides of the equation, simplifying it to gh = 0.5v².
Step 7: Rearrange the equation to solve for v²: v² = 2gh.
Step 8: Substitute the values for g (9.8 m/s²) and h (2 m): v² = 2 * 9.8 * 2.
Step 9: Calculate the right side: v² = 39.2.
Step 10: Take the square root of 39.2 to find v: v = √39.2.
Step 11: Calculate the square root to find the speed: v ≈ 6.26 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 height and kinetic energy (0.5mv²) at the lowest point of the swing.
Gravitational Acceleration – The constant acceleration due to gravity (approximately 9.8 m/s²) that affects the pendulum's motion.