The mass of an elevator is 4000 kg. Starting from rest how much distance will it rise in 2s, if the tension in the cable is 56kN ?

Options

A. 3m
B. 4m
C. 8m
D. 16m

Answer

To solve the problem step by step, we will follow these steps:

### Step 1: Identify the Given Data
- Mass of the elevator (m) = 4000 kg
- Tension in the cable (T) = 56 kN = 56000 N (since 1 kN = 1000 N)
- Time (t) = 2 seconds
- Initial velocity (u) = 0 m/s (starting from rest)

### Step 2: Calculate the Weight of the Elevator
The weight (W) of the elevator can be calculated using the formula:
\[ W = m \cdot g \]
where \( g \) is the acceleration due to gravity (approximately \( 9.81 \, \text{m/s}^2 \)).

Calculating the weight:
\[ W = 4000 \, \text{kg} \cdot 9.81 \, \text{m/s}^2 = 39240 \, \text{N} \]

### Step 3: Determine the Net Force Acting on the Elevator
The net force (F_net) acting on the elevator can be calculated using:
\[ F_{\text{net}} = T - W \]
Substituting the values:
\[ F_{\text{net}} = 56000 \, \text{N} - 39240 \, \text{N} = 16760 \, \text{N} \]

### Step 4: Calculate the Acceleration of the Elevator
Using Newton's second law of motion:
\[ F_{\text{net}} = m \cdot a \]
We can rearrange this to find acceleration (a):
\[ a = \frac{F_{\text{net}}}{m} \]
Substituting the values:
\[ a = \frac{16760 \, \text{N}}{4000 \, \text{kg}} = 4.19 \, \text{m/s}^2 \]

### Step 5: Use the Equation of Motion to Find the Distance
We will use the second equation of motion to find the distance (s):
\[ s = ut + \frac{1}{2} a t^2 \]
Since the initial velocity (u) is 0:
\[ s = 0 + \frac{1}{2} \cdot 4.19 \, \text{m/s}^2 \cdot (2 \, \text{s})^2 \]
Calculating the distance:
\[ s = \frac{1}{2} \cdot 4.19 \cdot 4 = 8.38 \, \text{m} \]

### Final Answer
The elevator will rise approximately **8.38 meters** in 2 seconds.

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