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

0.0035 J
0.0035 J

0.00175 J
0.00175 J

0.007 J
0.007 J

0.014 J
0.014 J

1 answer

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