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, 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 = 56,000 N
- Time (t) = 2 s
- Acceleration due to gravity (g) = 10 m/s² (assuming standard value)

### Step 2: Calculate the weight of the elevator
The weight (W) of the elevator can be calculated using the formula:
\[ W = m \cdot g \]
\[ W = 4000 \, \text{kg} \cdot 10 \, \text{m/s}^2 = 40,000 \, \text{N} \]

### Step 3: Calculate the net force acting on the elevator
The net force (F_net) can be calculated by subtracting the weight of the elevator from the tension in the cable:
\[ F_{\text{net}} = T - W \]
\[ F_{\text{net}} = 56,000 \, \text{N} - 40,000 \, \text{N} = 16,000 \, \text{N} \]

### Step 4: Calculate the acceleration of the elevator
Using Newton's second law, we can find the acceleration (a) of the elevator:
\[ F_{\text{net}} = m \cdot a \]
\[ 16,000 \, \text{N} = 4000 \, \text{kg} \cdot a \]
\[ a = \frac{16,000 \, \text{N}}{4000 \, \text{kg}} = 4 \, \text{m/s}^2 \]

### Step 5: Calculate the distance traveled by the elevator
Since the elevator starts from rest, the initial velocity (u) is 0. We can use the equation of motion to find the distance (s):
\[ s = u \cdot t + \frac{1}{2} a t^2 \]
Substituting the known values:
\[ s = 0 \cdot 2 + \frac{1}{2} \cdot 4 \cdot (2)^2 \]
\[ s = 0 + \frac{1}{2} \cdot 4 \cdot 4 \]
\[ s = 0 + 8 = 8 \, \text{m} \]

### Final Answer
The distance the elevator will rise in 2 seconds is **8 meters**.

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