Two concurrent forces have a maximum resultant of 45 and minimum of 5.What is the magnitude of each these force
Draw a parallelogram where the diagonals have those lengths.
Then just find the sides of the parallelogram.
a + b = 45
a - b = 5
solve the system ... elimination recommended
To find the magnitude of each of the concurrent forces, we need to determine the sum of the forces at both the maximum and minimum resultant values.
At the maximum resultant, the forces are fully additive, resulting in the sum of the magnitudes. So, we have:
Magnitude of Force 1 + Magnitude of Force 2 = Maximum Resultant = 45
At the minimum resultant, the forces are fully subtractive, resulting in the difference between the magnitudes. So, we have:
Magnitude of Force 1 - Magnitude of Force 2 = Minimum Resultant = 5
With these two equations, we can solve for the magnitudes of the forces:
From the equation: Magnitude of Force 1 + Magnitude of Force 2 = 45
We can rearrange it to solve for Magnitude of Force 1:
Magnitude of Force 1 = 45 - Magnitude of Force 2
Substituting this value into the second equation:
(45 - Magnitude of Force 2) - Magnitude of Force 2 = 5
Simplifying the equation:
45 - 2 * Magnitude of Force 2 = 5
- 2 * Magnitude of Force 2 = 5 - 45
- 2 * Magnitude of Force 2 = -40
Magnitude of Force 2 = -40 / -2
Magnitude of Force 2 = 20
Now, substituting the value of Magnitude of Force 2 back into the first equation, we can find the Magnitude of Force 1:
Magnitude of Force 1 = 45 - 20
Magnitude of Force 1 = 25
Therefore, the magnitude of Force 1 is 25 units and the magnitude of Force 2 is 20 units.