Question

Two identical blocks are connected by a lightweight string that passes over a lightweight pulley that can rotate about its axle with negligible friction. The two-block system is released from rest and the blocks accelerate. Which of the following correctly relates the potential energy gained by the block 1-Earth system |∆U1| to the potential energy lost by the block 2-Earth system |∆U2| and provides correct evidence?

Answer 1

In a frictionless system with massless string and pulley, the potential energy lost by block 2 is equal to the potential energy gained by block 1 due to the conservation of energy principle, resulting in |∆U1| = |∆U2|.

Step-by-step explanation:

The question relates to the concept of conservation of energy in a physics context, specifically involving a system of two blocks connected by a string and a pulley. According to the conservation of energy, the potential energy lost by block 2 as it falls must be equal to the potential energy gained by block 1 as it is raised, assuming there is no energy loss to friction or air resistance and the pulley is massless and frictionless. This is represented by the equation |∆U1| = |∆U2|.

To understand this better, when block 2 falls, it loses gravitational potential energy (U) which is given by the product of its mass (m), the acceleration due to gravity (g), and the change in height (h): |∆U2| = mgh. Simultaneously, block 1 gains the same amount of gravitational potential energy as it is raised by the same height, hence |∆U1| = mgh. Since we are dealing with ideal conditions (massless string, frictionless pulley), the system is mechanically isolated, and energy is conserved throughout the process.

Answer 2

The potential energy gained by the block 1-Earth system |∆U1| is equal to the potential energy lost by the block 2-Earth system |∆U2|. This is known as the law of conservation of energy, which states that energy cannot be created or destroyed, only transferred or converted from one form to another. In this case, the potential energy stored in block 2 at the start of the experiment is transferred to block 1 as they move and accelerate. The sum of the potential energy of the two-block system at the start of the experiment is equal to the sum of the kinetic energy and potential energy of the system at any point during the experiment. This relationship can be expressed mathematically as follows:

|∆U1| = |∆U2|

where |∆U1| is the potential energy gained by the block 1-Earth system and |∆U2| is the potential energy lost by the block 2-Earth system.