Force is defined as mass times acceleration. Starting with SI bas...

Question

Force is defined as mass times acceleration. Starting with SI base
units, derive a unit for force. Using SI prefixes, suggest a convenient unit for the force resulting from a collision with a 10-ton
trailer truck moving at 55 mi per hour and for the force resulting
from the collision of a molecule of mass around 10 - 20 kgmoving
almost at the speed of light (3 * 108 m>s) with the wall of its container. (Assume a 1-second deceleration time for both collisions.)

Accepted Answer

Hi everyone here we have a question that says in classical mechanics, kinetic energy is to find as the half mass times the square of speed, derive the unit for energy. Starting with S. I. Base units using S. I prefixes suggest convenient unit for the kinetic energy of a car weighing £2500 moving at 45 MPH, and the kinetic energy of an electron moving at 35% of the speed of light. The mass of an electron equals 9.11 times 10 to the negative 31 kg. And the speed of light equals 3.0 times 10 to the eight m per second. So we're gonna start with our £2,500 car and we're going to change it to the S. I. Unit. So kilograms, so times one kg over £2.. pounds will cancel out. That will equal 1,136. kg. Next we're going to take our 45 miles per hour, Times 1.609 km over one mile Times 10 to the 3rd meters over one kilometer times one hour over 60 minutes, Times one min 1 min over 60 seconds. And our miles are going to cancel out. Our kilometers are going to cancel out our Minutes are going to cancel out and our hours are going to cancel out and that's going to leave us with 20.11 m/s energy equals one half times m B squared. So energy is going to equal 1/ Times 1.13 Times 10 to the 3rd, kilograms Times 20.11 m/s squared. So we need to look at our exponents here to find a convenient unit of measurement. So we have 10 to the third, Plus 10 to the first Equals 10 to the 4th. So a convenient unit would be kilo and this is energy. So kill a jewel. Next we have the speed of light, So that equals 0. Times three times 10 to the 8th meters per second Equals 1.05 times 10 to the 8th. So e equals one half times 9.11 times 10 to the negative 31st. Kill a jewel or kilograms Times 1.05 times 10 to the 8th squared. So that if we look at our exponents here, we have 10 to the negative 31 plus 10 to the eighth and it's squared, so plus another 10 to the eighth and that equals 10 to the negative 15th. So a convenient unit would be Finito and it is energy. So 50 jewels. So, our convenient units here are kilo jewels and jewels. Thank you for watching. Bye

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