Question Video: Finding the Ratio between the Kinetic Energies of Two Moving Bodies Mathematics

A body of mass 170 metric tons was moving at 72 km/h and a second body of mass 850 g was moving at 5,000 m/s. Determine the ratio of the kinetic energy of the second body to that of the first one.

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Video Transcript

A body of mass 170 metric tons was moving at 72 kilometers per hour and a second body of mass 850 grams was moving at 5,000 meters per second. Determine the ratio of the kinetic energy of the second body to that of the first one.

In order to answer this question, we will begin by finding the kinetic energy of each body. We know that this can be calculated using the formula a half 𝑚𝑉 squared, where 𝑚 is the mass of the body and 𝑉 is its velocity. The standard units that we use to measure these are kilograms and meters per second, and the standard units for kinetic energy are joules.

We are told that the first body has a mass of 170 metric tons and was moving at a velocity of 72 kilometers per hour. There are 1,000 kilograms in one metric ton. This means that the first body has a mass of 170,000 kilograms. We know that there are 1,000 meters in one kilometer and 3,600 seconds in one hour. We can therefore convert 72 kilometers per hour into meters per second by multiplying 72 by 1,000 over 3,600. This is the same as multiplying by 10 and then dividing by 36 or simply dividing by 3.6.

The first body is therefore traveling at 20 meters per second. Its kinetic energy is therefore equal to a half multiplied by 170,000 multiplied by 20 squared. This is equal to 34,000,000. The first body has a kinetic energy of 34,000,000 joules. We are told that the second body has a mass of 850 grams and is traveling at 5,000 meters per second. As there are 1,000 grams in a kilogram, we can rewrite the mass as 0.85 kilograms. The kinetic energy of this body is equal to one-half multiplied by 0.85 multiplied by 5,000 squared. This is equal to 10,625,000. The kinetic energy of the second body is 10,625,000 joules.

We are asked to determine the ratio of the kinetic energy of the second body to that of the first one. Since both values are clearly divisible by 1,000, we can write the ratio as 10,625 to 34,000. Dividing both sides of the ratio by 34,000, the left-hand side simplifies to five sixteenths. The right-hand side is simply equal to one. We can then multiply both sides of this by 16, giving us the ratio five to 16.

The ratio of the kinetic energy of the second body to that of the first one is five to 16.

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