Two forces whose magnitude are in ratio of3:5 give a resultant of 35N if the angle of inclination be 60 degree calculate magnitude of each force
15.25
To solve this problem, we can use the concept of vector addition.
Let's assume the magnitude of the first force is 3x units and the magnitude of the second force is 5x units. So we have:
First force magnitude = 3x
Second force magnitude = 5x
The resultant of the two forces is 35N. From the given information, we know that the angle of inclination between the forces is 60 degrees.
To find the magnitudes of the forces, we can use the following formula:
Resultant = √(First force magnitude² + Second force magnitude² + 2 × First force magnitude × Second force magnitude × cosθ)
Replacing the values we have:
35 = √((3x)² + (5x)² + 2 × 3x × 5x × cos60)
Let's simplify this expression:
35 = √(9x² + 25x² + 30x²)
35 = √(64x²)
35 = 8x
Now, let's solve for x:
x = 35/8
x = 4.375
Now, substitute the value of x back into the magnitudes:
First force magnitude = 3x = 3 * 4.375 = 13.125 N
Second force magnitude = 5x = 5 * 4.375 = 21.875 N
Therefore, the magnitude of the first force is 13.125 N, and the magnitude of the second force is 21.875 N.
To calculate the magnitude of each force, we can follow these steps:
Step 1: We'll let the magnitude of the first force be 3x (since the ratio is given as 3:5) and the magnitude of the second force be 5x.
Step 2: We'll use the formula for finding the resultant of two forces: R² = F₁² + F₂² + 2F₁F₂cosθ, where R is the resultant, F₁ and F₂ are the magnitudes of the forces, and θ is the angle of inclination between them.
Step 3: Substitute the known values into the formula. The resultant (R) is given as 35N, and the angle of inclination (θ) is given as 60 degrees. We can now solve the equation:
35² = (3x)² + (5x)² + 2(3x)(5x)cos60°
Step 4: Simplify the equation:
1225 = 9x² + 25x² + 30x²
1225 = 64x²
Step 5: Solve for x by taking the square root of both sides:
x = √(1225/64)
x ≈ 5
Step 6: Now, substitute the value of x back into the expressions for the forces:
Force 1 = 3x = 3 * 5 = 15 N
Force 2 = 5x = 5 * 5 = 25 N
Therefore, the magnitude of the first force is 15 N and the magnitude of the second force is 25 N.
A/B=3/5
Let A=3x and B=5x and resultant being r
r=¡Ì(3x)2 +(5x2) +2*3x*5xcos@
35=¡Ì9x2+25x2+15x2
So,35=¡Ì49x2
35=7x
X=5N