Final answer:
The set of forces 10, 20, 40 cannot have a resultant force of zero because the sum of the smaller two forces (10 and 20) is not equal to or greater than the larger force (40). This violates the Triangle Inequality Theorem that is applied when considering vector addition of forces.
Step-by-step explanation:
The question is concerned with understanding when the resultant force acting on a point can or cannot be zero by looking at different sets of forces. This type of problem involves the concept of vector addition, which is used to calculate the resultant force of multiple vectors (forces).
For the resultant of a set of forces to be zero, the forces must be able to balance each other out. This means that in the two-dimensional plane, resultant forces in perpendicular directions must sum to zero. When given magnitudes of forces without specific directions, the Triangle Inequality Theorem can be used. This theorem implies that the sum of the lengths of any two sides of a triangle must be greater than or equal to the length of the third side. If we apply this to forces, it means for three forces to balance each other, any two forces must add up to be equal or greater than the third force.
- The sets 10, 10, 10 and 10, 20, 20 can form a triangle (or be balanced if we assume forces in opposite directions).
- The set 10, 10, 20 can also form a triangle as the sum of the smaller forces equals the greater force.
- However, the set 10, 20, 40 cannot form a triangle because no combination of the smaller two can sum to the larger one (10+20 is less than 40), hence they cannot balance out to a zero resultant.
Therefore, the set of forces that cannot have a resultant force of zero is 10, 20, 40.