A solid cone rolls down a slope. If its height is h, what is the speed of the co

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Question: A solid cone rolls down a slope. If its height is h, what is the speed of the cone at the bottom?

Options:

Correct Answer: √(2gh)

Solution:

Using conservation of energy, the potential energy mgh converts to kinetic energy. For a solid cone, the final speed at the bottom is v = √(2gh).

A solid cone rolls down a slope. If its height is h, what is the speed of the cone at the bottom?

A solid cone rolls down a slope. If its height is h, what is the speed of the cone at the bottom?

Step 1: Understand that the cone starts at a height 'h' on the slope.
Step 2: Recognize that at the top, the cone has potential energy due to its height, which is calculated as 'mgh' (where 'm' is mass, 'g' is gravity, and 'h' is height).
Step 3: Know that as the cone rolls down, this potential energy converts into kinetic energy.
Step 4: The kinetic energy of the cone at the bottom can be expressed as 'KE = 1/2 mv^2' (where 'v' is the speed of the cone).
Step 5: Set the potential energy equal to the kinetic energy: mgh = 1/2 mv^2.
Step 6: Cancel 'm' from both sides of the equation since it appears in both terms: gh = 1/2 v^2.
Step 7: Multiply both sides by 2 to eliminate the fraction: 2gh = v^2.
Step 8: Take the square root of both sides to solve for 'v': v = √(2gh).

Conservation of Energy – The principle that energy cannot be created or destroyed, only transformed from one form to another.
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 (1/2)mv².
Rolling Motion – The motion of an object that rolls without slipping, which involves both translational and rotational kinetic energy.