To predict the kinetic energy of the second marble, we can use the relationship between mass and kinetic energy. Kinetic energy (KE) is given by the equation:
\[ KE = \frac{1}{2} m v^2 \]
where \( m \) is mass and \( v \) is velocity.
From the information given:
- The first marble has a mass of 4.8 grams (0.0048 kg) and a kinetic energy of 0.0035 J.
- The second marble has a mass of 2.4 grams (0.0024 kg).
Since kinetic energy is directly proportional to mass (assuming the velocity is constant for both marbles), we can set up a proportion:
\[ \frac{KE_1}{KE_2} = \frac{m_1}{m_2} \]
Substituting the known values:
\[ \frac{0.0035 \text{ J}}{KE_2} = \frac{0.0048 \text{ kg}}{0.0024 \text{ kg}} \]
Calculating the ratio of masses:
\[ \frac{0.0048}{0.0024} = 2 \]
So we can rewrite the equation:
\[ \frac{0.0035}{KE_2} = 2 \]
This implies:
\[ KE_2 = \frac{0.0035 \text{ J}}{2} = 0.00175 \text{ J} \]
Thus, the best prediction for the kinetic energy of the second marble at the end of the plane is:
0.00175 J