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

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

A 2 kg block 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 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 * 5 m.
Step 5: Calculate the potential energy: 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 = 0.5 * mv².
Step 7: Set the potential energy equal to the kinetic energy: 98 Joules = 0.5 * 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 = √98.
Step 10: 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.
Frictionless Surfaces – Recognizing that the absence of friction simplifies the energy transformation process.