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An elevator system in a tall building consists of a 800-kg car and a 950-kg counterweight joined by a light cable of constant length that passes over a pulley of mass 280kg . The pulley, called a sheave, is a solid cylinder of radius 0.700m turning on a horizontal axle. The cable does not slip on the sheave. A number n of people, each of mass 80.0kg , are riding in the elevator car, moving upward at 3.00m/s and approaching the floor where the car should stop. As an energy-conservation measure, a computer disconnects the elevator motor at just the right moment so that the sheave-car-counterweight system then coasts freely without friction and comes to rest at the floor desired. There it is caught by a simple latch rather than by a massive brake(d) n=0 .

Answer :

An elevator system in a tall building consists of a 800-kg car and a 950-kg counterweight joined by a light cable of constant length that passes over a pulley of mass 280kg since n=0, the presence of people does not affect the calculation in this case. The system consists only of the car, counterweight, and pulley.

When n=0, there are no passengers in the lift vehicle. In this example, the system's entire mass consists of merely the vehicle, counterweight, and pulley. Let us examine the situation:

The total mechanical energy (E_total) can be expressed as the sum of the kinetic energy (KE) and potential energy (PE) of the system:

E_total = KE + PE

KE_initial = (1/2) * (m_car + m_counterweight + n * m_person) * [tex]v_{initial}^2[/tex]

KE_initial = (1/2) * (m_car + m_counterweight) * [tex]v_{initial}^2[/tex]

E_total = KE_initial + PE_initial = KE_final + PE_final

KE_initial + PE_initial = 0

Now,

(1/2) * (m_car + m_counterweight) * [tex]v_{initial}^2[/tex] + PE_initial = 0

The length of the cable is given by:

L = 2π * r_pulley

h = L - (r_car + r_counterweight)

We can compute the change in height (h) and the initial potential energy (PE_initial) by substituting the supplied numbers.

Thus, because n=0, the existence of persons in this scenario has no effect on the computation. The vehicle, counterweight, and pulley are the sole components of the system.

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