QuestionMay 1, 2025

Compare and contrast gravitational potentia l energy and elastic potential energy. they have in common?What is different about them? __

Compare and contrast gravitational potentia l energy and elastic potential energy. they have in common?What is different about them? __
Compare and contrast gravitational potentia l energy and elastic potential energy. they have in common?What is different about them? __

Solution
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Answer

Common: Both store energy based on position/state and convert to kinetic energy. ### Different: Gravitational depends on mgh, elastic depends on \frac{1}{2}kx^2. Explanation 1. Define gravitational potential energy Gravitational potential energy is the energy stored in an object due to its position relative to a gravitational field. **Formula: U_g = mgh**, where m is mass, g is gravitational acceleration, and h is height. 2. Define elastic potential energy Elastic potential energy is the energy stored in an object when it is stretched or compressed. **Formula: U_e = \frac{1}{2}kx^2**, where k is the spring constant and x is the displacement from equilibrium. 3. Compare similarities Both are forms of potential energy, depend on the object's state (position or deformation), and can be converted into kinetic energy. 4. Contrast differences Gravitational potential energy depends on mass and height in a gravitational field, while elastic potential energy depends on the stiffness of the material (k) and deformation (x).

Explanation

1. Define gravitational potential energy<br /> Gravitational potential energy is the energy stored in an object due to its position relative to a gravitational field. **Formula: $U_g = mgh$**, where $m$ is mass, $g$ is gravitational acceleration, and $h$ is height.<br /><br />2. Define elastic potential energy<br /> Elastic potential energy is the energy stored in an object when it is stretched or compressed. **Formula: $U_e = \frac{1}{2}kx^2$**, where $k$ is the spring constant and $x$ is the displacement from equilibrium.<br /><br />3. Compare similarities<br /> Both are forms of potential energy, depend on the object's state (position or deformation), and can be converted into kinetic energy.<br /><br />4. Contrast differences<br /> Gravitational potential energy depends on mass and height in a gravitational field, while elastic potential energy depends on the stiffness of the material ($k$) and deformation ($x$).
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