A rock of mass m and a rock of mass 2m are both released from rest at the same height and fee no air resistance as they fall. Which statements about these rocks are true? (there may be more than one!) EXPLAIN HOW YOU KNOW THEY ARE TRUE AND EXPLAIN WHY THE OTHERS ARE WRONG!!!(a) Both have the same initial gravitational potential (b) Both have the same kinetic energy when they reach the ground (c) Both reach the ground at the same speed. (d) When it hits the ground, the heavier rock has 4 times the kinetic energy of the lighter one.
Good fight.
To determine which statements are true, let's analyze each option:
(a) Both have the same initial gravitational potential:
This statement is true. Both rocks are released from rest at the same height, which means they have the same initial gravitational potential energy. The gravitational potential energy depends on the height and the mass of the object. Since both rocks are at the same height, their initial gravitational potential energy is the same.
(b) Both have the same kinetic energy when they reach the ground:
This statement is false. The kinetic energy of an object depends on its mass and velocity. Since the second rock has twice the mass of the first rock, and both rocks fall from the same height, their velocities will be different when they reach the ground. Therefore, their kinetic energies will be different.
(c) Both reach the ground at the same speed:
This statement is true. The Law of Conservation of Energy tells us that the total mechanical energy (sum of kinetic and potential energy) of a system is conserved. As the rocks fall, potential energy is converted into kinetic energy. Since the rocks have the same starting height, they experience the same decrease in potential energy. As a result, both rocks will have the same final kinetic energy, and therefore, the same speed when they reach the ground.
(d) When it hits the ground, the heavier rock has 4 times the kinetic energy of the lighter one:
This statement is false. The kinetic energy of an object is proportional to the square of its velocity and directly proportional to its mass. Since the heavier rock has twice the mass of the lighter one, it will have twice the kinetic energy at the same speed. It will not have four times the kinetic energy.
In summary:
(a) is true because both rocks have the same initial gravitational potential energy.
(b) is false because the two rocks will have different kinetic energies when they reach the ground.
(c) is true because both rocks reach the ground with the same speed.
(d) is false because the heavier rock has twice the kinetic energy, not four times, compared to the lighter rock.