To analyze the potential and kinetic energy of the cars at point X and at the bottom of the racetrack, we can use the formulas for potential energy (PE) and kinetic energy (KE):
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Potential Energy (PE) = mgh, where:
- m = mass (in kilograms)
- g = acceleration due to gravity (approximately 9.81 m/s²)
- h = height above the reference point
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Kinetic Energy (KE) = 0.5mv², where:
- m = mass (in kilograms)
- v = velocity (which will depend on how much potential energy has been converted into kinetic energy as the car moves down the track)
Given that the car is being placed at the same height (point X) regardless of its mass, the potential energy at point X can be calculated as follows:
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For the 500-gram car (0.5 kg): PE = 0.5 kg * g * h
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For the 700-gram car (0.7 kg): PE = 0.7 kg * g * h
The 700-gram car will indeed have more potential energy at point X because its mass is higher, assuming the height h remains the same.
At the bottom of the racetrack, the potential energy will be converted into kinetic energy. The total mechanical energy (potential energy at the top) will convert into kinetic energy (at the bottom) assuming no energy losses due to friction or air resistance.
Since both cars would convert their respective potential energies at the top to kinetic energies at the bottom without losses, the 700-gram car will have more kinetic energy at the bottom as compared to the 500-gram car.
Thus, the correct response is:
C. A 700-gram car would have more potential energy at point X and more kinetic energy at the bottom of the racetrack.
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