Question

velocity (m/s) kinetic energy (j)
1 1
2 4
3 9
4 16
what is the difference of the kinetic energy, in joules, of the 5 - gram marble and the smaller marble when b rolling at a velocity of 5 meters per second?
enter your answer in the response box.

Explanation:

Step1: Find the mass of the smaller marble

From the table, when \(v = 1m/s\), \(KE=1J\). Using the formula \(KE=\frac{1}{2}mv^{2}\), substituting \(v = 1m/s\) and \(KE = 1J\) into \(KE=\frac{1}{2}mv^{2}\), we get \(1=\frac{1}{2}m\times(1)^{2}\), so \(m = 2g\).

Step2: Calculate the kinetic energy of the 5 - gram marble

Using the formula \(KE=\frac{1}{2}mv^{2}\), with \(m = 5g=5\times10^{- 3}kg\) and \(v = 5m/s\). Then \(KE_{1}=\frac{1}{2}\times(5\times10^{-3})\times(5)^{2}=\frac{1}{2}\times5\times10^{-3}\times25=\frac{125}{2}\times10^{-3}=0.0625J\)

Step3: Calculate the kinetic energy of the 2 - gram marble

Using the formula \(KE=\frac{1}{2}mv^{2}\), with \(m = 2g = 2\times10^{-3}kg\) and \(v = 5m/s\). Then \(KE_{2}=\frac{1}{2}\times(2\times10^{-3})\times(5)^{2}=\frac{1}{2}\times2\times10^{-3}\times25=25\times10^{-3}=0.025J\)

Step4: Calculate the difference in kinetic energy

\(\Delta KE=KE_{1}-KE_{2}\)
\(\Delta KE=0.0625 - 0.025=0.0375J\)

Answer:

\(0.0375\)