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?
Well, when it comes to marble physics, it seems like the marbles are on a roll! Now, let's get down to predicting the kinetic energy of that second marble. Since the mass of the second marble is half of the first marble (2.4 grams), we can predict that its kinetic energy will also be half of the first marble's (0.0035 Joules). So, drumroll please, my best prediction is that the kinetic energy of the second marble will be approximately 0.00175 Joules. Just keep rolling with those physics calculations, my friend!
To determine the best prediction for the kinetic energy of the second marble, we can make use of the principle of conservation of energy. According to this principle, the total mechanical energy of a system remains constant as long as there are no external forces acting on it.
In this case, the only change in energy is due to the difference in mass between the two marbles. The kinetic energy (KE) of an object is given by the equation:
KE = (1/2) * mass * velocity^2
Since the first marble has a mass of 4.8 grams and a known kinetic energy of 0.0035 Joules, we can rearrange the equation to solve for its velocity:
velocity_1 = √(2 * KE / mass_1)
velocity_1 = √(2 * 0.0035 J / 0.0048 kg)
velocity_1 ≈ 1.63 m/s
Now, we can use the velocity_1 value to predict the kinetic energy of the second marble, which has a mass of 2.4 grams:
KE_2 = (1/2) * mass_2 * velocity_1^2
KE_2 = (1/2) * 0.0024 kg * (1.63 m/s)^2
KE_2 ≈ 0.0020 J
Therefore, the best prediction for the kinetic energy of the second marble at the end of the plane is approximately 0.0020 Joules.
To predict the kinetic energy of the second marble, we can use conservation of energy. According to the law of conservation of energy, the total mechanical energy of a system remains constant, assuming no external forces are acting on it.
Since both marbles are rolled down the same inclined plane, we can assume that the difference in potential energy (due to their difference in mass) is converted into kinetic energy. Therefore, the kinetic energy of the second marble can be predicted based on the ratio of their masses.
The ratio of the masses of the two marbles is 4.8 grams to 2.4 grams, which simplifies to 2:1.
Using this ratio, we can predict that the kinetic energy of the second marble at the end of the plane will be half of that of the first marble.
Hence, the best prediction for the kinetic energy of the second marble at the end of the plane is 0.0035 Joules divided by 2, which is 0.00175 Joules.