Question

Given a half-Atwood machine (two objects with given masses connected by a rope wound around a massive pulley, one pulled horizontally across a table by the rope, the other pulled downward by gravity), the moment of inertia and radius of the pulley, and the coefficient of friction for the object on the table, using the conservation of energy determine the speed of the object on the table after it has moved a given distance (hint: what object changes potential energy, what is the work done by the non-conservative force of friction, what are the kinetic energies for all 3 objects?)

Answer 1

In a half-Atwood machine, the conservation of energy can be used to determine the speed of the object on the table after it has moved a given distance.

Step-by-step explanation:

In a half-Atwood machine, the conservation of energy can be used to determine the speed of the object on the table after it has moved a given distance. The object on the table changes potential energy, while the object hanging from the pulley changes gravitational potential energy. The work done by the non-conservative force of friction can be calculated using the equation W = f × d.

To determine the speed of the object on the table, you need to equate the change in potential energy to the work done by friction and the kinetic energy of the object. The equation is:

m (1 - μ g d) v² = m g d

Where, m is the mass of the object, μ is the coefficient of friction, g is the acceleration due to gravity, and d is the distance the object has moved.