To predict the kinetic energy of the second marble based on the kinetic energy of the first marble, we can use the relationship between mass and kinetic energy. Kinetic energy (KE) is given by the formula:
\[ KE = \frac{1}{2} mv^2 \]
From the problem, we know that the first marble has a mass of 4.8 grams and a kinetic energy of 0.0035 Joules. The second marble has half the mass (2.4 grams) of the first marble.
Since kinetic energy is proportional to mass when dropping from the same height (and if we assume they roll down without any other forces acting, like friction), we can find the kinetic energy of the second marble using the ratio of their masses.
Let's calculate the expected kinetic energy of the second marble:
The mass ratio of the two marbles is: \[ \text{Mass Ratio} = \frac{2.4 , \text{g}}{4.8 , \text{g}} = \frac{1}{2} \]
We can then predict the kinetic energy of the second marble: \[ KE_2 = KE_1 \times \frac{2.4}{4.8} = 0.0035 , \text{J} \times \frac{1}{2} = 0.00175 , \text{J} \]
Thus, the best prediction for the kinetic energy of the second marble at the end of the plane is:
0.00175 J
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