Four forces act on an object, given by
A = 47.3 N east,
B = 36.3 N north,
C = 86.7 N west,
and
D = 72.7 N south.
(Assume east and north are directed along the +x-axis and +y-axis, respectively.)
I don't mind helping to find answers, but I resent having to provide the questions as well.
What is the direction of the force? (Enter your answer in degrees counterclockwise from the +x-axis.)
thats the question sorry
F = A+B+C+D = (47.3-86.7) i + (36.3-72.7) j = -39.4i -36.4j
the direction is θ where tanθ = -36.4/-39.4
θ = 222.73°
To find the net force acting on the object, we need to add up all the individual forces together. Since forces are vector quantities, we need to consider both their magnitudes and directions.
Let's break down each force into its components:
A = 47.3 N east = (47.3 N, 0 N)
B = 36.3 N north = (0 N, 36.3 N)
C = 86.7 N west = (-86.7 N, 0 N)
D = 72.7 N south = (0 N, -72.7 N)
Now, we can add up the components of each force separately. The x-component is obtained by adding the magnitudes of the eastward and westward forces, and the y-component is obtained by adding the magnitudes of the northward and southward forces.
Summing the x-components:
Ax + Cx = 47.3 N + (-86.7 N) = -39.4 N
Summing the y-components:
By + Dy = 36.3 N + (-72.7 N) = -36.4 N
Therefore, the net force acting on the object is approximately (-39.4 N, -36.4 N) or, in polar form, approximately 51.7 N at an angle of 212.6 degrees counterclockwise from the positive x-axis.