lenny wrote the steps he used to find the mass of an object with 400 j of energy moving at a velocity of 8…

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.

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.

Answer

Explanation:

Step1: Recall kinetic - energy formula

The formula for kinetic energy is $K = \frac{1}{2}mv^{2}$, where $K$ is kinetic energy, $m$ is mass, and $v$ is velocity. Rearranging for $m$ gives $m=\frac{2K}{v^{2}}$.

Step2: Analyze Lenny's steps

Lenny has $K = 400\ J$ and $v = 8\ m/s$. First, he correctly finds $v^{2}=(8\ m/s)^{2}=64\ m^{2}/s^{2}$ in Step 1. In Step 2, he divides $K$ by $v^{2}$ which is wrong. According to the formula $m=\frac{2K}{v^{2}}$, he should first multiply $K$ by 2 and then divide by $v^{2}$. In Step 3, he divides the result of Step 2 by 2. But the correct formula $m=\frac{2K}{v^{2}}$ means he should have multiplied the result of the correct operation (after multiplying $K$ by 2) by 1 (not divide by 2). In fact, the error is in Step 2. He should have multiplied 400 J by 2 first and then divided by $64\ m^{2}/s^{2}$, not just divide 400 J by $64\ m^{2}/s^{2}$.

Answer:

In Step 2, he should have multiplied 400 J by 2 and then divided by $64\ m^{2}/s^{2}$ instead of dividing 400 J by $64\ m^{2}/s^{2}$. So the answer is: In Step 2, he should have multiplied 400 J by 2 instead of dividing 400 J by $64\ m^{2}/s^{2}$.