Now, plug in the known values for "KE" ["kinetic energy"] and "m" ["mass"] ; and solve for "v". ______________________________________________________ Explanation: _____________________________________________________ The formula is: KE = (½) * (m) * (v²) ; _____________________________________
"Kinetic energy" = (½) * (mass) * (velocity , "squared") ________________________________________________ Note: Velocity is similar to speed, in that velocity means "speed and direction"; however, if you "square" a negative number, you will get a "positive"; since: a "negative" multiplied by a "negative" equals a "positive". ____________________________________________ So, we have the formula: ___________________________________ KE = (½) * (m) * (v²) ; to solve for "(v)" ; velocity, which is very similar to the "speed"; ___________________________________________________ we arrange the formula ; __________________________________________________ (KE) = (½) * (m) * (v²) ; ↔ (½)*(m)* (v²) = (KE) ; ___________________________________________________
→ We have: (½)*(m)* (v²) = (KE) ; we isolate, "m" (mass) on one side of the equation: ______________________________________________________
→ We divide each side of the equation by: "[(½)* (m)]" ; ___________________________________________________
→ v² = 2 KE / m _______________________________________________________ Take the "square root" of each side of the equation ; _______________________________________________________ → √ (v²) = √ { 2*(KE) ] / m } ________________________________________________________
→ v = √ { 2*(KE) ] / m } ;
Now, plug in the known values for "KE" ["kinetic energy"] and "m" ["mass"]; and solve for "v". ______________________________________________________
The charge of the copper nucleus is 29 times the charge of one proton: the charge of the electron is and their separation is
The magnitude of the electrostatic force between them is given by: where is the Coulomb's constant. If we substitute the numbers, we find (we can ignore the negative sign of the electron charge, since we are interested only in the magnitude of the force)
The kilogram-meter per second (kg · m/s or kg · m · s -1 ) is the standard unit of momentum . Reduced to base units in the International System of Units ( SI ), a kilogram-meter per second is the equivalent of a newton-second (N · s), which is the SI unit of impulse .
is the Coulomb's constant. If we substitute the numbers, we find (we can ignore the negative sign of the electron charge, since we are interested only in the magnitude of the force)
