Does the potential energy of an object near the surface of the Earth change if it moves with constant velocity in the horizontal direction? What if the object is gradually raised in the vertical direction?
No, the potential energy of the object does not change. The potential energy of an object near the Earth's surface is given by mgh, which depends on its height. Since moving horizontally does not change the height of the object, its potential energy remains constant.
Yes, the potential energy increases. When the object is gradually raised in the vertical direction, its height above the Earth's surface increases. As potential energy is directly proportional to height (mgh), raising the object to a greater height results in an increase in its potential energy.
Explanation
The textbook establishes that the potential energy of an object near the Earth's surface is calculated as mgh, meaning it is entirely dependent on the object's height. For part (i), horizontal motion does not alter the height (h), so the potential energy remains unchanged. For part (ii), gradually raising the object vertically increases its height (h), and since potential energy is directly proportional to height, the potential energy increases accordingly.