To solve for the net force ($\Sigma F$) and acceleration ($a$) acting on the object, let's analyze the forces in each direction.

Step 1: Break Down Forces

• Vertical Forces:

  • Upward: 2.5 N
  • Downward: 1 N
  • Net vertical force: $2.5 \, \text{N} - 1 \, \text{N} = 1.5 \, \text{N}$ (upward)

• Horizontal Forces:

  • Rightward: 1 N
  • Leftward: 1 N
  • Net horizontal force: $1 \, \text{N} - 1 \, \text{N} = 0 \, \text{N}$

Since there's no net force in the horizontal direction, the net force is purely vertical.

Step 2: Calculate $\Sigma F$

The net force ($\Sigma F$) is $1.5 \, \text{N}$ upward.

Step 3: Calculate Acceleration $a$

Using Newton's second law: $a = \frac{\Sigma F}{m}$ where $m = 8 \, \text{kg}$.

Substitute the values: $a = \frac{1.5 \, \text{N}}{8 \, \text{kg}} = 0.1875 \, \text{m/s}^2$

Summary

• $\Sigma F = 1.5 \, \text{N}$ (upward)
• $a = 0.1875 \, \text{m/s}^2$ (upward)

Would you like more details on the calculations or have any questions?

Related Questions

1. How would the net force change if the mass increased?
2. What happens to the acceleration if an additional horizontal force is applied?
3. How would we calculate the force if we only knew the acceleration and mass?
4. What if the object had a different mass; how would that impact the acceleration?
5. Can the direction of acceleration differ from the direction of net force?

Tip

Remember, net force is the vector sum of all forces acting on an object, considering both magnitude and direction.