Vector subtraction (F1 - F2) is a special case of vector addition, since F1- F2 = F1 + (-F2). Use the data (magnitude and direction) of F1 and F2 obtained in measurement 1 to find out the magnitude and direction of the resultant vector of F1 - F2.
The data is:
F1: 200g and 30 degrees. F2 = 200g at 120 degrees.
To find the magnitude and direction of the resultant vector of F1 - F2, you will need to follow these steps:
Step 1: Convert the given magnitudes into vector components.
- F1: With a magnitude of 200g and a direction of 30 degrees, we can break it down into its x and y components using trigonometry.
- F1x = 200g * cos(30 degrees)
- F1y = 200g * sin(30 degrees)
- F1x = 200g * 0.866 (rounded to 3 decimal places)
- F1y = 200g * 0.5 (rounded to 1 decimal place)
- F2: With a magnitude of 200g and a direction of 120 degrees, we can break it down into its x and y components using trigonometry.
- F2x = 200g * cos(120 degrees)
- F2y = 200g * sin(120 degrees)
- F2x = 200g * -0.5 (rounded to 1 decimal place)
- F2y = 200g * 0.866 (rounded to 3 decimal places)
Step 2: Subtract the corresponding components to get the resultant vector components.
- F1x - F2x = (200g * 0.866) - (200g * -0.5) = 346.4g
- F1y - F2y = (200g * 0.5) - (200g * 0.866) = -135.2g
Step 3: Calculate the magnitude of the resultant vector using the Pythagorean theorem.
- Magnitude = sqrt((F1x - F2x)^2 + (F1y - F2y)^2)
- Magnitude = sqrt((346.4g)^2 + (-135.2g)^2)
- Magnitude = sqrt(119952.96g^2 + 18270.04g^2)
- Magnitude = sqrt(138223.00g^2)
- Magnitude ≈ 371.6g (rounded to 1 decimal place)
Step 4: Calculate the direction of the resultant vector.
- Direction = atan((F1y - F2y) / (F1x - F2x))
- Direction = atan((-135.2g) / 346.4g) ≈ -21.2 degrees (rounded to 1 decimal place)
Therefore, the magnitude of the resultant vector of F1 - F2 is approximately 371.6g, and its direction is approximately -21.2 degrees.