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
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
Solution
The gravitational potential energy (PE) of an object can be calculated using the formula:
PE = m * g * h
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 (which is the sum of its kinetic and potential energy), and it starts at rest (so its initial kinetic energy is 0), we can say that its initial potential energy is also 500 J. This means that the mass of the object can be calculated as:
m = PE / (g * h) = 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 = m * g * h = 1.02 kg * 9.8 m/s² * 10 m = 100 J (approximately)
So, when the object has fallen to a height of 10 meters, its gravitational potential energy will be approximately 100 J.
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