Answer:
Step-by-step explanation:
The kinetic energy of an object is directly proportional to its mass and velocity. Therefore, to increase the kinetic energy of the marble, we need to increase either its mass or its velocity, or both. In this case, the student wants to increase the kinetic energy of the marble by increasing its mass.
To determine the optimal mass and size of the third marble, we need to consider the properties of the track and the gravitational potential energy of the marble. The gravitational potential energy of an object is directly proportional to its mass and the height it is raised above the ground. As the marble rolls down the track, it loses potential energy and gains kinetic energy, so the optimal mass of the marble will depend on the height of the track and the desired final speed of the marble.
If the track has a steep incline and the desired final speed of the marble is high, then a marble with a larger mass will have a greater kinetic energy than a marble with a smaller mass. However, if the track has a gentler slope or the desired final speed of the marble is relatively low, then a marble with a smaller mass may be sufficient to achieve the desired kinetic energy.
In terms of size, the third marble should be similar in size to the ceramic and steel marbles in order to fit properly on the track and roll smoothly. The size of the marble will not have a significant impact on its kinetic energy as long as its mass is increased sufficiently.
Therefore, to increase the kinetic energy of the marble, the third marble should be larger and heavier than both the ceramic and steel marbles, but of a similar size to fit properly on the track. The optimal mass and size will depend on the height and slope of the track and the desired final speed of the marble.