Two forces act concurrently on point P. One force is 85 N in a direction 35 degrees north of east. The second 95 N force acting at an angle of 227 degrees, what is the magnitude and direction of the resultant ?
R = 85N @ 35o + 95N @ 227o.
X = Hor. = 85*cos35+95*cos227=4.84 N.
Y = Ver. = 85*sin35+95*sin227=-20.7 N.
tanA = Y/X = -20.7/4.84 = -4.27856
A = -76.8o,CW = 103.2o,CCW = Direction.
Mag. = X/cosA = 4.84 / cos103.2=21.2 N.
r =
To find the magnitude and direction of the resultant force, we can use vector addition. We can break down each force into its horizontal and vertical components.
First, we need to find the horizontal and vertical components of the first force of 85 N. To do this, we can use trigonometry. The horizontal component (Fx1) can be found by multiplying the magnitude of the force (85 N) by the cosine of the angle (35 degrees).
Fx1 = 85 N * cos(35 degrees) = 69.618 N
The vertical component (Fy1) can be found by multiplying the magnitude of the force (85 N) by the sine of the angle (35 degrees).
Fy1 = 85 N * sin(35 degrees) = 47.665 N
Next, we need to find the horizontal and vertical components of the second force of 95 N. Again, we can use trigonometry. However, we need to consider that the angle given is 227 degrees clockwise from the positive x-axis. To make it counterclockwise from the positive x-axis, we subtract it from 360 degrees.
θ2 = 360 degrees - 227 degrees = 133 degrees
The horizontal component (Fx2) can be found by multiplying the magnitude of the force (95 N) by the cosine of the angle (133 degrees).
Fx2 = 95 N * cos(133 degrees) = -92.664 N (negative because it points in the negative x-direction)
The vertical component (Fy2) can be found by multiplying the magnitude of the force (95 N) by the sine of the angle (133 degrees).
Fy2 = 95 N * sin(133 degrees) = 43.843 N
Now, we can find the resultant components by summing up the horizontal and vertical components of both forces.
Rx = Fx1 + Fx2 = 69.618 N + (-92.664 N) = -23.046 N
Ry = Fy1 + Fy2 = 47.665 N + 43.843 N = 91.508 N
To find the magnitude of the resultant force (R), we can use the Pythagorean theorem:
R = sqrt(Rx^2 + Ry^2)
R = sqrt((-23.046 N)^2 + (91.508 N)^2)
R = sqrt(530.276 N^2 + 8390.576 N^2)
R = sqrt(8920.852 N^2)
R = 94.45 N (rounded to two decimal places)
To find the direction (θR) of the resultant force, we can use trigonometry. The angle will be measured counterclockwise from the positive x-axis.
θR = arctan(Ry / Rx)
θR = arctan(91.508 N / (-23.046 N))
θR ≈ -74.32 degrees
However, since this angle is in the fourth quadrant, we need to add 180 degrees to get the resultant angle measured counterclockwise from the positive x-axis.
θR = -74.32 degrees + 180 degrees
θR ≈ 105.68 degrees
Therefore, the magnitude of the resultant force is approximately 94.45 N, and its direction is approximately 105.68 degrees counterclockwise from the positive x-axis.