An object starts at rest from a height of 50 meters. It's total energy is 500 J. The object begins a free-falling motion; there is no air resistance. When it has fallen to a height of 10 meters, it's gravitational potential energy will be J, and it's total amount of energy will be
Question
An object starts at rest from a height of 50 meters. It's total energy is 500 J. The object begins a free-falling motion; there is no air resistance. When it has fallen to a height of 10 meters, it's gravitational potential energy will be J, and it's total amount of energy will be
Solution
The gravitational potential energy (PE) of an object can be calculated using the formula PE = mgh, where m is the mass of the object, g is the acceleration due to gravity (approximately 9.8 m/s² on Earth), and h is the height of the object above the ground.
Given that the total energy of the object is 500 J when it is at a height of 50 meters, we can rearrange the formula to solve for mass: m = PE / gh = 500 J / (9.8 m/s² * 50 m) = 1.02 kg (approximately).
When the object has fallen to a height of 10 meters, its gravitational potential energy will be PE = mgh = 1.02 kg * 9.8 m/s² * 10 m = 100 J (approximately).
The total energy of the object remains constant throughout its motion because of the conservation of energy. This principle states that energy cannot be created or destroyed, only transferred or transformed. Therefore, the total energy of the object when it has fallen to a height of 10 meters will still be 500 J.
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