F1 5,3N upwards f2 2,2N upwards and f 3 10,7N downwards determine the resultant of the three forces using a sketch vector diagram and check your answer with the equation
To determine the resultant of the three forces F1, F2, and F3, we will first draw a sketch vector diagram.
Step 1: Draw a coordinate system.
Begin by drawing a set of axes to establish a coordinate system. Label the horizontal axis as 'x' and the vertical axis as 'y.'
Step 2: Draw the vectors.
Next, draw the vectors F1, F2, and F3 according to their magnitudes and directions.
- F1: The vector F1 has a magnitude of 5.3N and is directed upwards. Place the tail of the vector at the origin and draw an arrow pointing upwards, representing F1. Label this vector as F1.
- F2: The vector F2 has a magnitude of 2.2N and is also directed upwards. Place the tail of the vector at the tip of the F1 vector and draw an arrow pointing upwards, representing F2. Label this vector as F2.
- F3: The vector F3 has a magnitude of 10.7N and is directed downwards. Place the tail of the vector at the origin and draw an arrow pointing downwards, representing F3. Label this vector as F3.
Step 3: Find the resultant.
To find the resultant of the three forces, we can use the equation:
Resultant = F1 + F2 + F3
To calculate the resultant, add the magnitudes of the vectors in each component direction. The x-component is the sum of the horizontal components, while the y-component is the sum of the vertical components.
- x-component: Since F1 and F2 are directed upwards, and F3 is directed downwards, the x-components of F1 and F2 will cancel each other out, leaving only the x-component of F3.
x-component of F3 = 0N (no horizontal component)
- y-component: The y-components of F1 and F2 are both directed upwards, so we can add them together. The y-component of F3 is directed downwards, so we need to subtract it from the sum of F1 and F2.
y-component of F1 + y-component of F2 - y-component of F3 = 5.3N + 2.2N - 10.7N = -3.2N
Therefore, the resultant vector is a vector with a magnitude of 3.2N directed downwards (as the negative sign indicates).