Two forces 18N and 10N are inclined at right angle of 60° to each other. calculate (i) the resultant force (ii) the angle of resultant forces that makes the force of 10N.
are inclined at right angle of 60° to each other>> Hmmm. What is a right angle again?
Pls i need the solving
To calculate the resultant force (i), we can use the Pythagorean theorem to find the magnitude and trigonometry to find the angle.
Step 1: Find the horizontal and vertical components of each force using trigonometry.
For the 18N force:
Horizontal component = 18N * cos(60°) = 9N
Vertical component = 18N * sin(60°) = 15.588N
For the 10N force:
Horizontal component = 10N * cos(90°) = 0N
Vertical component = 10N * sin(90°) = 10N
Step 2: Add up the horizontal and vertical components separately.
Horizontal component: 9N + 0N = 9N
Vertical component: 15.588N + 10N = 25.588N
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force.
Resultant force = √(horizontal component^2 + vertical component^2)
Resultant force = √(9N^2 + 25.588N^2)
Resultant force = √(81N^2 + 655.344N^2)
Resultant force = √(736.344N^2)
Resultant force ≈ 27.11N
Therefore, the resultant force is approximately 27.11N.
To calculate the angle (ii) that the resultant force makes with the 10N force, we can use trigonometry.
Step 4: Calculate the angular component of the resultant force using trigonometry.
Tan(angle) = (vertical component of resultant force) / (horizontal component of resultant force)
Tan(angle) = 25.588N / 9N
angle = Tan^(-1)(25.588N / 9N)
angle ≈ 70.64°
Therefore, the angle of the resultant force that makes the force of 10N is approximately 70.64°.