Question

a student is trying to find the mass of a billiard ball while playing pool. the ball is moving at a velocity of 2.3m/s and has a kinetic energy of 0.45j. the students work is shown below, what did they do wrong? they forgot to square the velocity they forgot to take the square root they used the wrong equation to solve for mass they did not do anything wrong

Explanation:

Step1: Recall the 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. To solve for \(m\), we should rearrange the formula as \(m=\frac{2K}{v^{2}}\). If the student forgot to square the velocity (i.e., used \(m = \frac{2K}{v}\) instead of \(m=\frac{2K}{v^{2}}\)), they would get an incorrect result.

Step2: Analyze other options

• Taking the square root (\(m=\frac{2K}{\sqrt{v}}\)) is not part of the correct formula derivation from \(K=\frac{1}{2}mv^{2}\).
• The formula \(K = \frac{1}{2}mv^{2}\) is the correct equation for kinetic energy when solving for mass (after rearrangement \(m=\frac{2K}{v^{2}}\)).

Answer:

they forgot to square the velocity