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

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

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

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: Understand that the block starts with potential energy at the top and converts it to kinetic energy at the bottom.
Step 4: Use the formula for potential energy (PE) at the top: PE = mgh, where g is the acceleration due to gravity (approximately 9.81 m/s²).
Step 5: Calculate the potential energy at the top: PE = 2 kg * 9.81 m/s² * 5 m.
Step 6: Calculate the potential energy: PE = 2 * 9.81 * 5 = 98.1 Joules.
Step 7: At the bottom, all potential energy converts to kinetic energy (KE), which is given by the formula KE = 0.5 * mv².
Step 8: Set the potential energy equal to the kinetic energy: 98.1 Joules = 0.5 * 2 kg * v².
Step 9: Simplify the equation: 98.1 = 1 * v², so v² = 98.1.
Step 10: Take the square root of both sides to find v: v = sqrt(98.1).
Step 11: 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.
Motion on an Incline – Analyzing the motion of an object sliding down an incline, particularly under the influence of gravity.