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
0.007 J
0.007 J
0.014 J
0.014 J
0.00175 J
To predict the kinetic energy of the second marble, we can use the principle of conservation of energy. The total mechanical energy (potential energy + kinetic energy) remains constant throughout the motion. Since both marbles roll down the same inclined plane, they start with the same potential energy. Therefore, we can assume that the second marble will have the same amount of potential energy at the start of the plane as the first marble.
Since kinetic energy is given by the equation KE = 0.5 * mass * velocity^2, and both marbles reach the end of the plane with the same velocity, we can set up the following equation for the two marbles:
0.5 * mass1 * velocity1^2 = 0.5 * mass2 * velocity2^2
Plugging in the values, we get:
0.5 * 4.8 * 0.0035 = 0.5 * 2.4 * velocity2^2
Simplifying the equation:
8.4 * 10^-3 = 1.2 * velocity2^2
Dividing both sides by 1.2, we get:
velocity2^2 = 7 * 10^-3
Taking the square root of both sides:
velocity2 ≈ 0.0833 m/s
Now, we can calculate the kinetic energy of the second marble using the mass and velocity:
KE2 = 0.5 * 2.4 * (0.0833)^2
Calculating this, we get:
KE2 ≈ 0.007 Joules
Therefore, the best prediction for the kinetic energy of the second marble at the end of the plane is 0.007 J.