Two forces, F1 and F2 , act at a point. F1 has a magnitude of 8.80N and is directed at an angle of 64.0 degree above the negative x axis in the second quadrant. F2 has a magnitude of 7.00N and is directed at an angle of 52.8 degree below the negative x axis in the third quadrant.
1. What is the x component of the resultant force?
2. What is the y component of the resultant force?
3. What is the magnitude of the resultant force?
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1. -8.80 cos 64.0 -7.00 cos 52.8
2. 8.80 sin 64.0 - 7.00 sin 52.8
3. Take the square root of the sum of squares of the two components given above.
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To find the x and y components of the resultant force and the magnitude of the resultant force, we can use vector addition.
1. To find the x component of the resultant force (Rx), we need to find the sum of the x components of F1 and F2. We can use the formula:
Rx = F1x + F2x
To find F1x, we need to multiply the magnitude of F1 (8.80N) by the cosine of the angle (64.0 degrees) because the x component is adjacent to the angle. So, F1x = 8.80N * cos(64.0 degrees).
To find F2x, we need to multiply the magnitude of F2 (7.00N) by the cosine of the angle (180 degrees - 52.8 degrees) because the angle is in the third quadrant, which is equivalent to 180 degrees minus the given angle. So, F2x = 7.00N * cos(180 degrees - 52.8 degrees).
Calculate F1x and F2x, then add them together to find Rx.
2. To find the y component of the resultant force (Ry), we need to find the sum of the y components of F1 and F2. We can use the formula:
Ry = F1y + F2y
To find F1y, we need to multiply the magnitude of F1 (8.80N) by the sine of the angle (64.0 degrees) because the y component is opposite to the angle. So, F1y = 8.80N * sin(64.0 degrees).
To find F2y, we need to multiply the magnitude of F2 (7.00N) by the sine of the angle (180 degrees - 52.8 degrees) because the angle is in the third quadrant, which is equivalent to 180 degrees minus the given angle. So, F2y = 7.00N * sin(180 degrees - 52.8 degrees).
Calculate F1y and F2y, then add them together to find Ry.
3. To find the magnitude of the resultant force (R), we can use the Pythagorean theorem, which states that the square of the magnitude of the resultant force is equal to the sum of the squares of its x and y components. The formula is:
R^2 = Rx^2 + Ry^2
Calculate Rx and Ry from the previous steps, and then take the square root of their sum to find R.