To solve the problem in the image, we need to calculate the net acceleration of the elevator. Here are the steps:

Given:

• Weight of the elevator ($W$) = $50,000 \, \text{N}$
• Force acting upward ($F_{\text{up}}$) = $100,000 \, \text{N}$
• Gravitational acceleration ($g$) = $9.8 \, \text{m/s}^2$

Step 1: Find the mass of the elevator

The weight of the elevator is related to its mass by: $W = m g$ $m = \frac{W}{g} = \frac{50,000}{9.8} \approx 5102 \, \text{kg}$

Step 2: Calculate the net force

The net force ($F_{\text{net}}$) is the difference between the upward force and the weight: $F_{\text{net}} = F_{\text{up}} - W = 100,000 - 50,000 = 50,000 \, \text{N}$

Step 3: Calculate the acceleration

Using Newton's second law: $F_{\text{net}} = m a$ $a = \frac{F_{\text{net}}}{m} = \frac{50,000}{5102} \approx 9.8 \, \text{m/s}^2$

Since the upward force is greater than the weight, the acceleration is upward.

Final Answer:

The acceleration of the elevator while braking is: $\boxed{9.8 \, \text{m/s}^2 \, \text{up}}$

Would you like a deeper explanation of the concepts or assistance with similar problems?

Related Questions:

1. How does Newton's second law apply to vertical motion problems like this?
2. What would happen if the upward force equaled the weight of the elevator?
3. How would the acceleration change if the upward force was less than $50,000 \, \text{N}$?
4. What role does gravitational acceleration play in problems like these?
5. How can we determine the direction of acceleration in such problems?

Tip:

Always double-check whether the net force is in the same direction as the acceleration when solving force-related problems!