Forces with magnitudes of 45 N and 90 N act on an object at angles of 20 degrees and 115 degrees respectively, with the X-axis. Find the magnitude of the resultant of these forces.
convert to x-y components so they can be added:
45@20° = <42.29,15.39>
90@115° = <-38.04,81.57>
add them up to get
<4.25,96.96> = 97.05 @ 87.49°
To find the magnitude of the resultant of these forces, we can use vector addition.
Step 1: Convert the forces into their X and Y components.
- The force of 45 N has an angle of 20 degrees with the X-axis.
- X component: 45 N * cos(20°) = 41.00 N (rounded to two decimal places)
- Y component: 45 N * sin(20°) = 15.39 N (rounded to two decimal places)
- The force of 90 N has an angle of 115 degrees with the X-axis.
- X component: 90 N * cos(115°) = -43.60 N (rounded to two decimal places)
- Y component: 90 N * sin(115°) = 85.92 N (rounded to two decimal places)
Step 2: Add the X components and Y components separately.
- X component of the resultant = 41.00 N + (-43.60 N) = -2.60 N
- Y component of the resultant = 15.39 N + 85.92 N = 101.31 N
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant.
- Magnitude of the resultant = √((X component)^2 + (Y component)^2)
- Magnitude of the resultant = √((-2.60 N)^2 + (101.31 N)^2)
- Magnitude of the resultant ≈ 102.7 N (rounded to one decimal place)
Therefore, the magnitude of the resultant of the two forces is approximately 102.7 N.