Kinetic energy (KE) is directly proportional to mass, given by the formula:
\[ KE = \frac{1}{2} m v^2 \]
From the information provided, the first marble has a mass of 4.8 grams and a kinetic energy of 0.0035 Joules. We can find its energy-to-mass ratio:
\[ \text{Energy per gram} = \frac{KE}{\text{mass}} = \frac{0.0035 , \text{J}}{4.8 , \text{g}} \approx 0.0007292 , \text{J/g} \]
Now, let's calculate the expected kinetic energy of the second marble, which has a mass of 2.4 grams. Using the same energy-to-mass ratio:
\[ KE_{2.4g} = \text{Energy per gram} \times \text{mass} = 0.0007292 , \text{J/g} \times 2.4 , \text{g} \approx 0.00175 , \text{J} \]
Thus, the best prediction for the kinetic energy of the second marble at the end of the plane is:
0.00175 J