Question

An elevator starts from rest with a constant upward acceleration and moves 1 m in the first 1.9 s. A passenger in the elevator is holding a 5 kg bundle at the end of a vertical cord.
What is the tension in the cord as the ele- vator accelerates? The acceleration of gravity is 9.8 m/s2 .
Answer in units of N

Answer 1

An elevator starts from rest with a constant upward acceleration and moves 1 m in the first 1.9 s. A passenger in the elevator is holding a 5 kg bundle at the end of a vertical cord.

What is the tension in the cord as the elevator accelerates? The acceleration of gravity is 9.8 m/s².

Answer in units of N

Solution:

Let:

$$\begin{array}{l} h = 1 \, \text{m} \\ t = 1.9 \, \text{s} \\ m = 5 \, \text{kg} \\ g = 9.8 \, \text{m/s}^2 \\ \end{array}$$

F-?

$F = mg + ma$, were $a$-acceleration of elevator

$$\begin{array}{l} h = \frac{1}{2} a t^2 = 2 a = 2 h / t^2 \\ F = m \left( g + 2 h / t^2 \right) \\ F = 5 \left( 9.8 + 2 \cdot 1 / 1.9^2 \right) = 51.77 \, \text{N} \\ \end{array}$$

Answer: 51.77N