Let's analyze the problem to determine the correct acceleration.

Given:

1. Weight of the bucket $F_g = 200 \, \text{N}$ (downward force).
2. Tension in the rope $F_T = 220 \, \text{N}$ (upward force).
3. Mass of the bucket $m = 20 \, \text{kg}$.

Net Force $F_{\text{net}}$:

The net force is the difference between the upward force (tension) and the downward force (gravity).

$F_{\text{net}} = F_T - F_g$

Substitute the given values:

$F_{\text{net}} = 220 \, \text{N} - 200 \, \text{N} = 20 \, \text{N} \, \text{(upward)}.$

Acceleration $a$:

Using Newton's second law:

$F_{\text{net}} = m a$

Solve for $a$ (acceleration):

$a = \frac{F_{\text{net}}}{m}$

Substitute $F_{\text{net}} = 20 \, \text{N}$ and $m = 20 \, \text{kg}$:

$a = \frac{20 \, \text{N}}{20 \, \text{kg}} = 1 \, \text{m/s}^2.$

The direction of the acceleration is upward because the net force is upward.

Final Answer:

The bucket accelerates at 1 m/s² upward.

Do you need further clarification or details? Let me know!

Related Questions:

1. How would the acceleration change if the tension were 240 N?
2. What would happen if the tension in the rope were equal to the weight of the bucket?
3. If the tension in the rope were 180 N, what would the acceleration be?
4. How do you calculate the force of tension in a rope lifting an object at rest?
5. What is the relationship between net force and acceleration according to Newton’s laws?

Tip: Newton's Second Law $F = ma$ is essential for solving force and motion problems. Always determine the direction of forces carefully!