Three co-linear forces f1=45 N west,f2=63 N east and an unknown force f3 are applied to an object.the resultant of the three forces is 12 N west determine the magnitude and direction of the force f3 using algebraic calculations. Thank you indvance.
f1 = <-31.82,31.82>
f2 = <44.55,44.55>
r = <-8.49,8.49>
f3 = <x,y> where
-31.82+44.55+x = -8.49
31.82+44.44+y = 8.49
Now just find x and y.
How did you find f1,f2 and f3?
To determine the magnitude and direction of the unknown force F3, we can use the principle of vector addition.
Given:
F1 = 45 N west
F2 = 63 N east
Resultant force (Fres) = 12 N west
Step 1: Determine the net force acting on the object.
The net force is the vector sum of all the forces acting on the object. In this case, we have F1, F2, and F3.
Fres = F1 + F2 + F3
Step 2: Assign directions to the forces.
Since F1 and F3 are both west and F2 is east, we can assign positive and negative signs to represent their directions.
Let's assume F1 and F3 as negative, as they are directed west, and F2 as positive since it is directed east.
Step 3: Write the equation.
Fres = -(F1) + F2 + F3
Step 4: Substitute the given values.
12 N west = -(45 N) + 63 N + F3
Step 5: Solve for the unknown force F3.
Rearrange the equation to isolate F3:
F3 = 12 N - 63 N + 45 N
F3 = -6 N
So, the magnitude of the unknown force F3 is 6 N, and since it has the same direction as F1 and F3, it is directed west.
Hence, the unknown force F3 has a magnitude of 6 N and is directed west.
To determine the magnitude and direction of the force f3, we can use vector addition. Since the forces are in opposite directions (west and east), we can subtract them.
First, let's assign a positive direction as east and a negative direction as west. This means we will consider the force in the opposite direction as negative.
Given:
f1 = 45 N west (negative)
f2 = 63 N east (positive)
Resultant force = 12 N west (negative)
Using vector addition, we can write the equation:
f1 + f2 + f3 = 0
Substituting the given values:
-45 N + 63 N + f3 = 0
Rearranging the equation:
f3 = 45 N - 63 N
Simplifying:
f3 = -18 N
The magnitude of force f3 is 18 N, and since it is in the opposite direction of f1 and f2, it is also west.
Therefore, the magnitude of the force f3 is 18 N, and its direction is west.