Exercise 7.6
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? Ready to Go Beyond Work done on a system against its internal forces, such as gravitational, electric or magnetic forces, can result in a gain of the potential energy of the system. But this is not true for all internal forces. For example, work done against friction does not lead to a storage of energy. You will learn how to identify such forces in higher grades. Once again, consider an object with mass m which has been lifted to potential energy of the object kinetic energy of the object mechanical energy
Not cross-checked
NCERT prints no numerical answer for this exercise, so this working has not been cross-checked against the book.
NCERT’s answer
No; yes
Horizontal motion: No, the potential energy does not change. Gradual vertical raising: Yes, it increases.
\(\displaystyle U = mgh \) depends only on the height \(\displaystyle h \) above the Earth's surface.
Moving horizontally, \(\displaystyle h \) is unchanged, so \(\displaystyle U \) is unchanged. The gravitational force is perpendicular to the displacement here, so it does no work (Fig. $\displaystyle 7.6$).
Raising the object through a height \(\displaystyle \Delta h \) means doing work \(\displaystyle mg \times \Delta h \) against gravity, and that work appears as a gain in potential energy: \(\displaystyle \Delta U = mg\,\Delta h \).
