The problem in the image presents four situations in which forces act on a block resting on a frictionless surface. The question asks in which scenarios it is possible for the block to be:

1. Stationary (i.e., at rest, with no acceleration).
2. Moving with a constant velocity (i.e., no net acceleration but could still be in motion).

For both conditions, the net force on the block must be zero, following Newton's First Law (if the net force is zero, the object remains at rest or moves with constant velocity).

Let's analyze each situation:

1. Situation (1):

   • Forces $F_1$ and $F_2$ are acting in opposite directions.
   • If $F_1 = F_2$, the net force is zero. Hence, the block could either be stationary or moving with constant velocity.

2. Situation (2):

   • Forces $F_1$ and $F_2$ are acting in opposite directions, along the same line.
   • If $F_1 = F_2$, the net force is zero. Again, the block could either be stationary or moving with constant velocity.

3. Situation (3):

   • Three forces, $F_1$, $F_2$, and $F_3$, are acting in different directions.
   • To have no net force, the vector sum of these three forces must equal zero, which is only possible if their magnitudes and directions satisfy specific conditions (likely requiring equal magnitudes and opposite directions). So, this scenario is less likely unless carefully balanced.

4. Situation (4):

   • Forces $F_1$, $F_2$, and $F_3$ act at different angles.
   • Similarly, for the net force to be zero, the vector sum of these three forces must exactly cancel out. This setup makes it harder for the net force to be zero unless the magnitudes and directions are perfectly balanced, which is less likely in most practical cases.

Conclusion:

• Stationary or constant velocity:
  • Situations (1) and (2) could both result in the block being stationary or moving with constant velocity, provided the forces are equal and opposite.
  • Situations (3) and (4) would require very specific and unlikely conditions to result in zero net force.

Would you like further explanation on any specific part?

Here are some related questions for deeper understanding:

1. How do you calculate the resultant force in vector problems like this?
2. What is the significance of a frictionless surface in this context?
3. How can multiple forces in different directions lead to equilibrium?
4. How does Newton's First Law apply to these types of force scenarios?
5. What methods can be used to verify if the forces cancel each other out?

Tip: When forces are acting at angles, it's helpful to break them into components along the x- and y-axes to check for equilibrium.