Question

lenny wrote the steps he used to find the mass of an object with 400 j of energy moving at a velocity of 8 m/s. 1. find the square of 8 m/s, which is 64 m²/s². 2. divide kinetic energy, 400 j, by 64 m²/s², which is 6.25 j per m²/s². 3. divide 6.25 j per m²/s² by 2 to get a mass of 3.125 kg. which best describes lennys error? in step 1, he should have found the square - root of 400 j instead of squaring 8 m/s. in step 1, he should have multiplied 8 m/s by 2 instead of squaring it. in step 2, he should have divided 64 m²/s² by 400 j instead of dividing 400 j by 64 m²/s². in step 3, he should have multiplied 6.25 j per m²/s² by 2 instead of dividing it by 2

Explanation:

Step1: Recall kinetic - energy formula

The kinetic - energy formula is $K = \frac{1}{2}mv^{2}$, and we want to solve for $m$. Rearranging gives $m=\frac{2K}{v^{2}}$. In Step 1, when starting to solve for $m$ from $K=\frac{1}{2}mv^{2}$, the correct first step from the formula manipulation is to multiply both sides by 2 to get $2K = mv^{2}$, and then $m=\frac{2K}{v^{2}}$. Lenny's error was in Step 1, he should have multiplied the velocity by 2 (as part of getting the correct formula rearrangement for $m$) instead of squaring the velocity.

Answer:

In Step 1, he should have multiplied 8 m/s by 2 instead of squaring it.