Depending on the angle between them, those two forces can combine to produce
a resultant anywhere between 10N and 40N. The maximum of 40N occurs when
both forces act in exactly the same direction.
The maximum resultant occurs when the forces act in the same direction. Its magnitude is 15 N.
10N if both forces are in the same direction.
The min net force magnitude you can have is (20 - 12) = 8 N, when the two forces are directly opposite in directions. When the two forces align, the net force magnitude becomes the maximum, which is equal to (20 + 12) = 32 N. You can guess that the net force magnitude is somewhere between 8 N and 32 N, when the two forces are at an angle other than 0o or 180o. Let us say the larger force is A and the smaller force is B, at an angle, alpha, to one another. Then the net force magnitude, |C| = |A| + |B|*cos(alpha). The magnitude of C, |C|, depends solely on cos(alpha), since |A| and |B| are fixed. When alpha = 0o, |C|= |A| + |B| (maximal); when alpha = 180o, |C|= |A| - |B| (minimal). Note that max(cos(alpha))=1 and min(cos(alpha))=-1. ================================
The magnitude of the resultant force in the case of the concurrent forces in equilibrium.
Zero. Forces combine as vectors. The magnitude of the resultant force is equal to the sum of the magnitudes of the two combining forces only when the forces are parallel. Caveat: This does assume that the "maximum result" desired is a single force, such as would be relevant in producing the linear acceleration of a mass. If, for instance, one wanted to produce the maximum torque as a "result," the points (locations) where the forces were applied would make a difference and there are circumstances where torque would be maximized by oppositely directed forces.
The maximum resultant occurs when the forces act in the same direction. Its magnitude is 15 N.
The magnitude of a force is its 'size' or 'strength', regardless of its direction.
The magnitude of the resultant force in the case of the concurrent forces in equilibrium.
10N if both forces are in the same direction.
The min net force magnitude you can have is (20 - 12) = 8 N, when the two forces are directly opposite in directions. When the two forces align, the net force magnitude becomes the maximum, which is equal to (20 + 12) = 32 N. You can guess that the net force magnitude is somewhere between 8 N and 32 N, when the two forces are at an angle other than 0o or 180o. Let us say the larger force is A and the smaller force is B, at an angle, alpha, to one another. Then the net force magnitude, |C| = |A| + |B|*cos(alpha). The magnitude of C, |C|, depends solely on cos(alpha), since |A| and |B| are fixed. When alpha = 0o, |C|= |A| + |B| (maximal); when alpha = 180o, |C|= |A| - |B| (minimal). Note that max(cos(alpha))=1 and min(cos(alpha))=-1. ================================
All forces have direction and magnitude
The magnitude of the resultant force in the case of the concurrent forces in equilibrium.
Zero. Forces combine as vectors. The magnitude of the resultant force is equal to the sum of the magnitudes of the two combining forces only when the forces are parallel. Caveat: This does assume that the "maximum result" desired is a single force, such as would be relevant in producing the linear acceleration of a mass. If, for instance, one wanted to produce the maximum torque as a "result," the points (locations) where the forces were applied would make a difference and there are circumstances where torque would be maximized by oppositely directed forces.
A force is a vector quantity because it has both magnitude and direction.
In magnitude.
It depends on the magnitude of the forces.
No, the magnitude of the resulting force when forces are combined is at MOST equal to the sum of forces, this is when they are all in the same direction. Else its magnitude will always be less than the sum of magnitudes of the individual forces involved (some forces will be oposing or "fighting" others).