To find the kinetic energy of the second marble, we can use the relationship between mass and kinetic energy. The kinetic energy (KE) of an object is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
Where:
- \( KE \) is the kinetic energy,
- \( m \) is the mass,
- \( v \) is the velocity.
While we don't know the velocity of either marble, we can assume that if they roll down the same inclined plane, they will both experience the same potential energy conversion to kinetic energy along the incline assuming no energy is lost to friction or air resistance.
Given:
- For the first marble (mass \( m_1 = 4.8 \) grams, or 0.0048 kg), \( KE_1 = 0.0035 \) Joules.
- For the second marble (mass \( m_2 = 2.4 \) grams, or 0.0024 kg), we want to find \( KE_2 \).
The ratio of their kinetic energies will be proportional to their masses, based on the conservation of energy principle:
\[ \frac{KE_2}{KE_1} = \frac{m_2}{m_1} \]
Substituting in the values:
\[ \frac{KE_2}{0.0035} = \frac{0.0024}{0.0048} \]
Calculating the right side:
\[ \frac{0.0024}{0.0048} = \frac{1}{2} \]
This implies:
\[ KE_2 = KE_1 \cdot \frac{1}{2} = 0.0035 \cdot \frac{1}{2} = 0.00175 \text{ Joules} \]
Therefore, the best prediction for the kinetic energy of the second marble at the end of the plane is:
0.00175 J
0 answers