To determine the work done by the spring force on the block in each situation, we need to examine the initial and final positions and determine the direction of the spring force relative to the block's displacement.

Situation Analysis

1. Situation (a):

   • Initial position: $x = 3 \, \text{cm}$
   • Final position: $x = 2 \, \text{cm}$
   • The block moves from $x = 3 \, \text{cm}$ to $x = 2 \, \text{cm}$, which means it is moving toward the equilibrium position (compression is reducing).
   • The spring force is in the direction of the displacement (toward equilibrium), so work done is positive.

2. Situation (b):

   • Initial position: $x = 2 \, \text{cm}$
   • Final position: $x = 3 \, \text{cm}$
   • The block moves from $x = 2 \, \text{cm}$ to $x = 3 \, \text{cm}$, meaning it moves away from equilibrium.
   • The spring force is opposite to the displacement (since it tries to pull the block back to equilibrium), so work done is negative.

3. Situation (c):

   • Initial position: $x = -2 \, \text{cm}$
   • Final position: $x = 2 \, \text{cm}$
   • The block moves from $x = -2 \, \text{cm}$ to $x = 2 \, \text{cm}$, passing through the equilibrium point.
   • During this movement, the spring force direction changes at the equilibrium point, but overall the spring is providing force in the direction of the block’s motion on both sides of equilibrium.
   • Therefore, work done is positive.

Answers:

• (a) Positive
• (b) Negative
• (c) Positive

Would you like more detailed reasoning or have any questions?

Here are five related questions for further exploration:

1. How does Hooke's Law relate to the spring force in these examples?
2. What is the significance of the equilibrium position in determining work done by the spring?
3. How would the energy transfer differ if friction were present in these scenarios?
4. How can we calculate the exact amount of work done by the spring force if given a spring constant?
5. What happens to the kinetic energy of the block as it moves through each situation?

Tip: Remember that work done by a spring force is positive when the force direction aligns with the displacement and negative when they oppose each other.