A lamp hangs vertically from a cord in a descending elevator with a constant deceleration a. If the tension in the cord is T0, answer the following. (Use any variable or symbol stated above along with the following as necessary: g.)

(a) What is the lamp's mass?
m =

(b) What is the cord's tension when the elevator ascends with upward acceleration a?
Tf =

1.305

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To answer these questions, we can use Newton's second law of motion (F = ma) and the free-body diagram of the lamp.

(a) What is the lamp's mass?
To find the lamp's mass, we need to consider the forces acting on it when the elevator is in deceleration. The forces acting on the lamp are its weight (mg) and the tension in the cord (T0).

The net force acting on the lamp is equal to the mass of the lamp times its acceleration (F = ma). Considering the downward direction as positive, we have:
mg - T0 = ma

Rearranging the equation, we get:
m = (T0 + ma) / g

So, the lamp's mass is m = (T0 + ma) / g.

(b) What is the cord's tension when the elevator ascends with upward acceleration a?
When the elevator ascends with upward acceleration, we have to consider the forces acting on the lamp again. The forces acting on the lamp are its weight (mg) and the tension in the cord (Tf).

Using the same approach as before, the net force acting on the lamp is equal to the mass of the lamp times its acceleration. Considering the upward direction as positive, we have:
Tf - mg = ma

Rearranging the equation, we get:
Tf = mg + ma

So, the cord's tension when the elevator ascends with upward acceleration is Tf = mg + ma.