The problem involves a 90-kg worker pulling a rope in a pulley system to lift a 60-kg crate, with the worker applying a force of 1000 N. The question is to determine what happens in this scenario.

Given Data:

• Mass of the worker ($m_w$) = 90 kg
• Mass of the crate ($m_c$) = 60 kg
• Force applied by the worker ($F$) = 1000 N
• Acceleration due to gravity ($g$) = $10 \, \text{m/s}^2$

Step 1: Forces Acting on the Worker

The total downward force acting on the worker: $F_{\text{down, worker}} = m_w \cdot g = 90 \cdot 10 = 900 \, \text{N}$

The worker applies an upward pulling force of 1000 N. Since the worker pulls downward on the rope, the rope tension increases beyond the worker's weight.

Step 2: Forces Acting on the Crate

The crate experiences a gravitational force pulling it downward: $F_{\text{down, crate}} = m_c \cdot g = 60 \cdot 10 = 600 \, \text{N}$

The tension in the rope is now equal to the pulling force applied by the worker (1000 N).

Step 3: Net Force on the Crate

The net force ($F_{\text{net, crate}}$) on the crate: $F_{\text{net, crate}} = T - F_{\text{down, crate}}$ Substituting the values: $F_{\text{net, crate}} = 1000 - 600 = 400 \, \text{N}$

Step 4: Acceleration of the Crate

Using Newton’s second law ($F = m \cdot a$), the acceleration of the crate ($a_c$) is: $a_c = \frac{F_{\text{net, crate}}}{m_c} = \frac{400}{60} \approx 6.67 \, \text{m/s}^2$

Step 5: Movement of the Worker

The pulling force applied by the worker exceeds their own weight. Therefore, the worker will be lifted upwards with an acceleration. The net force ($F_{\text{net, worker}}$) on the worker is: $F_{\text{net, worker}} = F - F_{\text{down, worker}}$ Substituting the values: $F_{\text{net, worker}} = 1000 - 900 = 100 \, \text{N}$

The acceleration of the worker ($a_w$) is: $a_w = \frac{F_{\text{net, worker}}}{m_w} = \frac{100}{90} \approx 1.11 \, \text{m/s}^2$

Conclusion:

• The crate accelerates upwards with an acceleration of approximately $6.67 \, \text{m/s}^2$.
• The worker is lifted upwards with an acceleration of approximately $1.11 \, \text{m/s}^2$.

Would you like further details or a visual explanation of this scenario?

Follow-Up Questions:

1. What would happen if the applied force were less than 900 N?
2. How does the system behave if the worker's mass equals the crate's mass?
3. Can you derive the time taken for the crate to reach a certain height?
4. What happens if a second crate is added to the system?
5. How would the tension in the rope change if the worker stops applying force?

Tip:

Always analyze the net forces and accelerations independently for each body in such problems to understand the system's dynamics comprehensively.