find the resultant of each pair of forces acting on an object
a) forces of 7N east and 12N west
b) forces of 7N east and 12N north
I don't understand your question
you have no magnitude
12N north makes no sense
that's the way the question was presented
To find the resultant of a pair of forces acting on an object, you need to determine the net force acting on the object. This can be done by considering the magnitudes and directions of the individual forces.
a) To find the resultant of the forces of 7N east and 12N west, you can start by assigning positive and negative signs to the forces based on their directions. Let's assume east is positive and west is negative.
Force 1: 7N (east) = +7N
Force 2: 12N (west) = -12N
To find the resultant force, you need to add these forces together:
Resultant force = 7N + (-12N) = -5N
The resultant force is -5N, which means it has a magnitude of 5N and acts in the direction opposite to the net force. In this case, it acts west.
b) To find the resultant of the forces of 7N east and 12N north, you need to break down the forces into horizontal and vertical components.
Force 1: 7N (east)
The horizontal component of this force is simply 7N (east).
The vertical component is zero since the force is acting horizontally.
Force 2: 12N (north)
The horizontal component of this force is zero since the force is acting vertically.
The vertical component is 12N (north).
To find the resultant force, you need to add the horizontal and vertical components separately:
Horizontal component: 7N (east) + 0 = 7N (east)
Vertical component: 0 + 12N (north) = 12N (north)
Using these components, you can determine the magnitude and direction of the resultant force using vector addition (Pythagorean theorem and trigonometry). However, since you only asked for the resultant force, we can stop here.
Therefore, the resultant force is a vector with a magnitude of 7N (east) in the horizontal direction and 12N (north) in the vertical direction.