A person jumped out of a plane and began falling to the surface of the Earth at a rate of 9.8 m/s².The person and their equipment have a total mass of 95 kg.After 30 seconds they have reached a speed of 50 m/s with a kinetic energy store of energy of 118 750 J.During this fall the person has had a change in gravitational energy of 2.4 MJ.Calculate the energy transferred to the surroundings.
Question
A person jumped out of a plane and began falling to the surface of the Earth at a rate of 9.8 m/s².The person and their equipment have a total mass of 95 kg.After 30 seconds they have reached a speed of 50 m/s with a kinetic energy store of energy of 118 750 J.During this fall the person has had a change in gravitational energy of 2.4 MJ.Calculate the energy transferred to the surroundings.
Solution
To calculate the energy transferred to the surroundings, we first need to understand the energy changes that have occurred.
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The person has gained kinetic energy as they fall. This is given as 118,750 J.
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The person has also lost gravitational potential energy as they fall. This is given as 2.4 MJ, which is 2,400,000 J.
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The total energy change is the sum of the kinetic energy gained and the gravitational potential energy lost. So, the total energy change is 118,750 J + 2,400,000 J = 2,518,750 J.
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However, not all of this energy change is transferred to the surroundings. Some of it is used to increase the person's speed. The energy used to increase the person's speed can be calculated using the formula for kinetic energy, which is 0.5 * mass * speed^2.
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Substituting the given values into this formula gives 0.5 * 95 kg * (50 m/s)^2 = 118,750 J.
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Therefore, the energy transferred to the surroundings is the total energy change minus the energy used to increase the person's speed. So, the energy transferred to the surroundings is 2,518,750 J - 118,750 J = 2,400,000 J.
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