A 33 N force acting at 90° and a 44 N force at 60° are applied
concurrently at a point P. What is the magnitude and direction of the
resultant force?
Add the two forces as vectors. Adding the x and y components separately is an easy way to do it. Then the magnitude will be the square root of the sum of the squares of the sum of the force components.
To find the resultant force, we need to use the concept of vector addition. The magnitude and direction of the resultant force can be found by using the following steps:
Step 1: Resolve each force into its horizontal and vertical components.
- Force with magnitude 33 N at an angle of 90°:
- Horizontal component = 0 N (since it is perpendicular to the x-axis)
- Vertical component = 33 N (since it is parallel to the y-axis)
- Force with magnitude 44 N at an angle of 60°:
- Horizontal component = 44 N * cos(60°) = 22 N
- Vertical component = 44 N * sin(60°) = 38.084 N
Step 2: Add the horizontal and vertical components separately.
- Horizontal component: 0 N + 22 N = 22 N
- Vertical component: 33 N + 38.084 N = 71.084 N
Step 3: Use the Pythagorean theorem to find the magnitude of the resultant force.
- Magnitude of the resultant force = sqrt((22 N)^2 + (71.084 N)^2) = sqrt(484 N^2 + 5043.335856 N^2) ≈ 74.51 N
Step 4: Use trigonometry to find the direction of the resultant force.
- Angle = tan^(-1)((71.084 N)/(22 N))
- Angle ≈ 73.166°
Therefore, the magnitude of the resultant force is approximately 74.51 N and its direction is approximately 73.166°.
To find the magnitude and direction of the resultant force, we can use the concept of vector addition.
Step 1: Resolve the forces into their horizontal and vertical components.
For the 33 N force at 90°:
Horizontal component = 33 N * cos(90°) = 0 N
Vertical component = 33 N * sin(90°) = 33 N
For the 44 N force at 60°:
Horizontal component = 44 N * cos(60°) = 22 N
Vertical component = 44 N * sin(60°) = 38.04 N (rounded to two decimal places)
Step 2: Add the horizontal and vertical components separately to get the resultant components.
Horizontal component of the resultant force = 0 N + 22 N = 22 N
Vertical component of the resultant force = 33 N + 38.04 N ≈ 71.04 N (rounded to two decimal places)
Step 3: Calculate the magnitude and direction of the resultant force using the resultant components.
Magnitude of the resultant force = √(Horizontal component² + Vertical component²)
= √(22 N² + 71.04 N²) ≈ 74.09 N (rounded to two decimal places)
Direction of the resultant force = arctan(Vertical component / Horizontal component)
= arctan(71.04 N / 22 N) ≈ 73.62° (rounded to two decimal places)
Since both force vectors are in the first quadrant, the resultant force is also in the first quadrant. Therefore, the direction of the resultant force is 73.62° (rounded to two decimal places) above the positive x-axis.
So, the magnitude of the resultant force is approximately 74.09 N and its direction is approximately 73.62° above the positive x-axis.