Question

The Atwood's machine shown consists of two blocks connected by a light string that passes over a pulley of negligible mass and negligible friction. The blocks are released from rest, and the mass of block 1 is greater than the mass of block 2. Assume that the reference line of zero gravitational potential energy is the floor. Which of the following best represents the total gravitational potential energy and total kinetic energy of the block-block-earth system as a function of the height of block 1?

1) Gravitational potential energy increases and kinetic energy decreases
2) Gravitational potential energy decreases and kinetic energy increases
3) Gravitational potential energy and kinetic energy both increase
4) Gravitational potential energy and kinetic energy both decrease

Answer 1

In Atwood's machine scenario, the descending heavier block converts gravitational potential energy into kinetic energy, leading to a decrease in total potential energy and an increase in total kinetic energy of the system as block 1 lowers.

Step-by-step explanation:

When considering Atwood's machine situation of two blocks connected by a string with a pulley system, the fundamental principle involved is the conservation of mechanical energy. As block 1, which is heavier, descends, its gravitational potential energy (PEg) is converted into kinetic energy (KE). Conversely, as block 2 ascends, it gains PEg at the expense of losing KE. Thus, as block 1 descends and block 2 ascends, the total PEg of the system decreases while the total KE increases. Hence, the correct representation of the changes in the block-block-earth system as a function of the height of block 1 is: gravitational potential energy decreases and kinetic energy increases.