To compare the kinetic and potential energies of the two watermelons, we need to consider the following:
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Potential Energy (PE): This energy is determined by the height of an object above the ground, given by the formula: \[ PE = mgh \] where:
- \(m\) is the mass of the object,
- \(g\) is the acceleration due to gravity (\(9.81 , \text{m/s}^2\) on Earth),
- \(h\) is the height from which the object falls.
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Kinetic Energy (KE): This energy is determined by the speed of the object, given by the formula: \[ KE = \frac{1}{2}mv^2 \] where:
- \(m\) is the mass of the object,
- \(v\) is the speed of the object.
To perform a comparison, you'll need the masses \(m_1\) and \(m_2\) and speeds \(v_1\) and \(v_2\) of the two watermelons, as well as the height \(h\) from which they fell.
Steps to Compare Energies
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Calculate Potential Energy: If both watermelons fell from the same height, their potential energies can be compared using their masses: \[ PE_1 = m_1gh \quad \text{and} \quad PE_2 = m_2gh \] The watermelon with the greater mass will have more potential energy, assuming the heights are equal.
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Calculate Kinetic Energy: Use the masses and speeds to find kinetic energies: \[ KE_1 = \frac{1}{2}m_1v_1^2 \quad \text{and} \quad KE_2 = \frac{1}{2}m_2v_2^2 \] The watermelon with the greater mass and/or higher speed will have more kinetic energy.
Comparison Summary:
- If the watermelons have different masses, the one with the greater mass has more potential energy before falling.
- If both have the same height but different speeds upon reaching the ground, the one with the higher speed has more kinetic energy upon impact.
- At the moment of impact, potential energy decreases to zero (assuming they are at ground level), converting to kinetic energy.
If you provide the specific masses, speeds, and height information, I can help you perform the exact calculations!
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