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 lenny’s 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:

The formula for kinetic energy is \( KE=\frac{1}{2}mv^{2} \), where \( KE \) is kinetic energy, \( m \) is mass, and \( v \) is velocity. To solve for mass \( m \), we rearrange the formula to \( m = \frac{2KE}{v^{2}} \).

• Step 1: Squaring the velocity (\( v = 8 \, \text{m/s} \), \( v^{2}=64 \, \text{m}^2/\text{s}^2 \)) is correct.
• Step 2: Dividing \( KE = 400 \, \text{J} \) by \( v^{2}=64 \, \text{m}^2/\text{s}^2 \) (getting \( \frac{400}{64}=6.25 \)) is correct as it corresponds to \( \frac{KE}{v^{2}} \).
• Step 3: From the rearranged formula \( m=\frac{2KE}{v^{2}} \), after calculating \( \frac{KE}{v^{2}} = 6.25 \), we need to multiply by 2 (not divide) to get the mass. So Lenny's error is in Step 3 where he divided by 2 instead of multiplying by 2.

Answer:

In Step 3, he should have multiplied 6.25 J per \( \text{m}^2/\text{s}^2 \) by 2 instead of dividing it by 2.