Question

12 what is the mass of an object that has 324 j of ke when moving at 9 m/s?

Explanation:

Step1: Recall the kinetic energy formula

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

Step2: Rearrange the formula to solve for \(m\)

Starting with \(KE = \frac{1}{2}mv^{2}\), we can multiply both sides by \(2\) to get \(2KE=mv^{2}\). Then divide both sides by \(v^{2}\) to isolate \(m\), so \(m=\frac{2KE}{v^{2}}\).

Step3: Substitute the given values

We know \(KE = 324\space J\) and \(v = 9\space m/s\). Substituting these into the formula \(m=\frac{2\times324}{9^{2}}\).
First, calculate \(2\times324 = 648\) and \(9^{2}=81\). Then \(m=\frac{648}{81}\).

Step4: Calculate the value of \(m\)

\(\frac{648}{81}=8\space kg\)

Answer:

\(8\space kg\)