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Question Video: Finding the Gravitational Potential Energy of a Vertically Falling Body and Its Kinetic Energy at a Given Point Mathematics

A body of mass 4 kg fell vertically from a height of 28 m above the surface of the ground. Find its gravitational potential energy š‘ relative to the ground and its kinetic energy š‘‡ when it was 7 m above the ground. Consider the acceleration due to gravity to be 9.8 m/sĀ².

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Video Transcript

A body of mass four kilograms fell vertically from a height of 28 meters above the surface of the ground. Find its gravitational potential energy š‘ relative to the ground and its kinetic energy š‘‡ when it was seven meters above the ground. Consider the acceleration due to gravity to be 9.8 meters per second squared.

We are told in the question that a body of mass four kilograms falls vertically from a height of 28 meters above the ground. We are asked to find its potential energy š‘ and kinetic energy š‘‡ when it was seven meters above the ground.

We begin by recalling that the gravitational potential energy of an object is equal to š‘šš‘”ā„Ž. We multiply the mass of the object by the acceleration due to gravity by the vertical height. The kinetic energy of an object is equal to a half š‘šš‘£ squared, where once again š‘š is the mass and š‘£ is the velocity. The potential energy š‘ of the body when it was seven meters above the ground is therefore equal to four multiplied by 9.8 multiplied by seven. This is equal to 274.4. Since we have used the standard units of kilograms, meters per second squared, and meters, the potential energy will be measured in joules. š‘ is equal to 274.4 joules.

From the conservation of energy, we know that the increase in kinetic energy will be equal to the decrease in potential energy. And since the body fell from rest, the initial kinetic energy is equal to zero. The final kinetic energy that we are trying to calculate is therefore equal to the initial potential energy minus the final potential energy. The initial potential energy š‘ sub š‘– is equal to four multiplied by 9.8 multiplied by the height of 28 meters. This is equal to 1097.6. And the kinetic energy š‘‡ that we are trying to calculate is therefore equal to 1097.6 minus 274.4. This is equal to 823.2. The kinetic energy of the body when it was seven meters above the ground was 823.2 joules.

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