A 15.0 kg stone and a 150 kg stone are released from rest at the same height above the ground. There is no appreciable air drag.
Which of the following statements is or are true? (More than one statement may be true.)
A. Both stones have the same initial gravitational potential energy.
B. Both stones will have the same acceleration as they fall.
C. Both stones will have the same speed when they reach the ground.
D. Both stones will have the same kinetic energy when they reach the ground.
E. Both stones will reach the ground at the same time.
To determine which statements are true, let's break down the problem:
A. Both stones have the same initial gravitational potential energy.
To calculate the gravitational potential energy, we use the formula: potential energy (PE) = mass (m) * acceleration due to gravity (g) * height (h). Since both stones are released from the same height and the acceleration due to gravity is the same for all objects on Earth, their initial gravitational potential energy is indeed the same.
B. Both stones will have the same acceleration as they fall.
According to Newton's second law of motion, the acceleration of an object is given by the equation: acceleration (a) = net force (F) / mass (m). In this case, the only force acting on the stones is gravity, which is the same for both. Therefore, according to the equation, both stones will have the same acceleration as they fall.
C. Both stones will have the same speed when they reach the ground.
As the stones fall, they convert their initial gravitational potential energy into kinetic energy. The kinetic energy of an object is given by the equation: kinetic energy (KE) = 0.5 * mass (m) * velocity squared (v^2). Since both stones fall from the same height and have the same acceleration, they will both have the same speed (velocity) when they reach the ground.
D. Both stones will have the same kinetic energy when they reach the ground.
As mentioned before, the kinetic energy depends on mass and velocity. Therefore, since both stones have the same speed when they reach the ground, and their masses are different (15.0 kg and 150 kg), they will not have the same kinetic energy.
E. Both stones will reach the ground at the same time.
According to the principle of free fall, objects in a vacuum (without air resistance) will fall with the same acceleration regardless of their mass. So, both stones will reach the ground at the same time.
To summarize, the correct statements are:
A. Both stones have the same initial gravitational potential energy.
B. Both stones will have the same acceleration as they fall.
C. Both stones will have the same speed when they reach the ground.
E. Both stones will reach the ground at the same time.