Find the magnitude of the resultant force and the angle it makes with the positive x-axis. (Let a = 200 N and b = 300 N. Round your answers to one decimal place.)
Magnitude = ___ N
Angle= ____ degrees
the vector a is 60 degrees from the positive x axis, the vector b is on the negative x axis.
first break down the vectors into x and y components using cos and sin.
a = (200cos(60), 200sin(60) b = (300cos(180), 300sin(180)) y component of b will be zero
next add these two vectors
a+b = < 200cos(60) + 300cos(180), 200sin(60) + 0 > = <-200, 173.2>
the force is the magnitude of this vector
Force = sqrt[ -200^2 + 173.2^2 ] = 264.6N
To find the angle it helps to draw a+b and see where it is. We can see the vector points in the upper left quadrant (i don't know the numbers) so we can now use the x and y components along with the magnitude to draw a right triangle with the hypotenuse being the magnitude. The angle between the Y axis and the hypotenuse can be calculated using sin.
sin(x) =[x-component/hypotenuse]=200/264.6= 49.1
since this angle is between the Y-axis and the vector, and the question asks for the angle between the X-axis and the vector we simply add 90 degrees.
49.1 + 90 = 139.1
sorry i could not draw the picture. it really helps to understand the angle part if you see the triangle.
there's a well-known formulation to discover the importance (resultant tension)^2 = a^2 + b^2 - 2abcos(attitude between the vectors) the place a and b are the importance of the given vectors. permit r = the importance of the consequent tension. now we could pick to discover the attitude that r makes with the extra beneficial of the two forces (a=26N the extra beneficial one) in vector notation: vector r = vector a + vector b or vector b = vector r - vector a the above is a vector notation yet there's a importance notation for this one, too besides the incontrovertible fact that it differes from the consequent vector b^2 = r^2 + a^2 + 2racos(attitude between r and a) [notice there's a plus sign no longer minus] use this formulation to discover the attitude between r and a. (a, b and r are the importance of the vectors a,b and r respectively!) * * * * notice: i'm undecided bearing directly to the 2nd formulation. perhaps the the ultimate option one is: b^2 = r^2 + a^2 - 2racos(attitude between r and a) [there's a minus sign no longer plus] verify the two one in all them.