A student rolls two marbles down an inclined plane. One marble has a mass of 4.8 grams. The student calculates its kinetic energy to be 0.0035 Joules when it reaches the end of the plane. The second marble has a mass of 2.4 grams. What is the best prediction for its kinetic energy at the end of the plane?(1 point)

Responses

0.014 J
0.014 J

0.00175 J
0.00175 J

0.007 J
0.007 J

0.0035 J

1 answer

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