The problem asks to identify which set of three forces acting on an object cannot be in equilibrium.

1. Problem Description

The problem asks to identify which set of three forces acting on an object cannot be in equilibrium.

2. Solution Steps

For an object to be in equilibrium when subjected to three coplanar forces, the vector sum of the forces must be zero. This implies that the sum of any two forces must be greater than or equal to the magnitude of the third force, and less than or equal to their sum. In other words, the three forces must be able to form a triangle.

i. 10 N, 10 N, 10 N

10 + 10 >= 10, and 10 + 10 <=

2

0. This is possible.

ii. 8 N, 8 N, 10 N

8 + 8 >= 10, and 8 + 8 <=

1

6. This is possible.

iii. 10 N, 8 N, 10 N

10 + 8 >= 10, and 10 + 8 <=

1

8. This is possible.

iv. 1 N, 2 N, 3 N

1 + 2 >= 3 and 1 + 2 <=

3. The equality condition is met, meaning the three forces can be in equilibrium. They could be arranged such that the 1 N and 2 N forces act in the same direction, and the 3 N force acts in the opposite direction. This is possible.

v. 2 N, 3 N, 6 N

2 + 3 = 5, which is less than

6. Therefore, the sum of any two forces is not greater than or equal to the magnitude of the third force. Thus, equilibrium is not possible.

3. Final Answer

v. 2 N, 3 N, 6 N