The following forces act on a body:f1=5,3N upwards;f2=2,2N upwards and f3=10,7N downwards.determine the resultant of the three forces using vector addition
To determine the resultant of the three forces using vector addition, you need to add all three forces together by considering their magnitudes and directions.
Step 1: Represent the forces as vectors
For vector addition, it's essential to represent the forces as vectors. Vectors have both magnitude (size) and direction. In this case, let's consider upward forces as positive (+) and downward forces as negative (-).
f1 = 5.3 N upwards
f2 = 2.2 N upwards
f3 = 10.7 N downwards
Step 2: Assign coordinate axes
Next, assign coordinate axes to simplify the representation. In this case, let's consider the positive y-axis pointing upwards.
Step 3: Calculate the resultant vector
Now, add all three vectors together to find the resultant:
Resultant = f1 + f2 + f3
To do this, we'll break down the forces into their x-components and y-components.
Horizontal (x-components):
Since all the forces have purely vertical components, their horizontal components will be zero.
f1x = 0 N
f2x = 0 N
f3x = 0 N
Vertical (y-components):
To calculate the vertical components, we use the signs we assigned earlier.
f1y = +5.3 N upwards
f2y = +2.2 N upwards
f3y = -10.7 N downwards
Now add the vertical components together.
Resultant y-component = f1y + f2y + f3y
Resultant y-component = (5.3 N) + (2.2 N) + (-10.7 N)
Resultant y-component = -3.2 N downwards
Therefore, the resultant of the three forces is -3.2 N downwards.