A disk rolls down an incline. If the height of the incline is h, what is the spe

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Question: A disk rolls down an incline. If the height of the incline is h, what is the speed of the disk at the bottom assuming no energy losses?

Options:

Correct Answer: √(2gh)

Solution:

Using conservation of energy, potential energy at height h converts to kinetic energy at the bottom. The speed is √(2gh).

A disk rolls down an incline. If the height of the incline is h, what is the speed of the disk at the bottom assuming no energy losses?

A disk rolls down an incline. If the height of the incline is h, what is the speed of the disk at the bottom assuming no energy losses?

Step 1: Understand that the disk starts at a height 'h' on the incline.
Step 2: Recognize that at the top, the disk has potential energy due to its height.
Step 3: Know that potential energy (PE) can be calculated using the formula PE = mgh, where 'm' is mass, 'g' is the acceleration due to gravity, and 'h' is the height.
Step 4: As the disk rolls down, this potential energy converts into kinetic energy (KE) at the bottom of the incline.
Step 5: The formula for kinetic energy is KE = 0.5 * m * v^2, where 'v' is the speed of the disk.
Step 6: Since there are no energy losses, the potential energy at the top equals the kinetic energy at the bottom: mgh = 0.5 * m * v^2.
Step 7: Cancel the mass 'm' from both sides of the equation (since it is the same on both sides).
Step 8: You are left with gh = 0.5 * v^2.
Step 9: Multiply both sides by 2 to isolate v^2: 2gh = v^2.
Step 10: Take the square root of both sides to find the speed: v = √(2gh).

Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another.
Kinetic and Potential Energy – Understanding the relationship between potential energy at height and kinetic energy at speed.
Motion on Inclines – Analyzing the motion of objects rolling down inclines and the effects of gravity.