Question

Figure 5-22 shows overhead views of four situations in which forces act on a block that lies on a frictionless floor. If the force magnitudes are chosen properly, in which situations is it possible that the block is

(a) stationary and

(b) moving with a constant velocity?

Short answer

1. Situations 2 and 4 in which the block is stationary
2. Situations1 and 3 in which the block is moving with constant velocity

Step-by-step solution

Given information:

Figure 5-22 shows overhead views of four situations in which forces act on a block that lies on a frictionless floor.

Understanding the given information

The problem is based on the calculation of resultant force. The resultant force is described as the total amount of force acting on the object or body along with the direction of the body. The resultant force is zero when the object is at rest or it is traveling with the same velocity as the object.

(a)In which situation the block is stationary

Generally, for the block to be stationary the direction of the forces acting on it should be exactly opposite to each other and of equal magnitude else the block will move with a constant velocity in the resultant direction of the applied forces.

In figure 2, the direction of the force ${\text{F}}_{\text{1}}$and ${\text{F}}_{\text{2}}$are opposite with respect to each other hand so by applying equal magnitude of the two forces the block will remain stationary.

In figure 4, the resultant force between the combination of the two forces will always have the direction opposite to one of the three forces ${\text{F}}_{\text{1}}$, ${\text{F}}_{\text{2}}$, and ${\text{F}}_{\text{3}}$and hence by applying the appropriate magnitude of the forces the block will remain stationary

(b)In which situation the block is moving with constant velocity

In figure 1, the forces ${\text{F}}_1$and ${\text{F}}_{\text{2}}$are not opposite irrespective of the magnitude of the two forces, the block will move with a constant velocity in the direction of the resultant force.

In figure 3, the direction of the forces ${\text{F}}_{\text{1}}$, ${\text{F}}_{\text{2}}$, and ${\text{F}}_{\text{3}}$or resultant forces between the combination of these forces is not opposite and hence irrespective of the magnitude of the forces applied the block will move with a constant velocity in the direction of the resultant force.