Question

Four forces are acting on a point mass located at the origin of a two-dimensional cartesian coordinate system. The first force has a magnitude of 10.0 N and makes a 30° angle with the positive x-axis. The second force has a magnitude of 15.0 N and makes a 135° angle with the positive x-axis. The third force has a magnitude of 20.0 N and makes an angle of 240° with the positive x-axis. The fourth force has a magnitude of 25.0 N and makes a 315° with the positive x-axis. a) Find the magnitude of the resultant force (in Newtons) acting on the object. b) What angle (in degrees) does the resultant force make with the positive x-axis?

Answer 1

here,

F1 = 10 * ( cos(30) i +sin(30) j )N

F1 = 8.66 i N + 5 j N

F2 = 15 * ( cos(135) i +sin(135) j)

F2 = - 10.6 i N + 10.6 J N

F3 = 20 * ( cos(240 ) i + sin(240) j)

F3 = - 10 N i - 17.32 j N

F4 = 25 * ( cos(315) i + sin(315) j)

F4 = 17.68 i N - 17.68 j N

the net force , F = F1 + F2 + F3 + F4

F = 5.74 i N - 19.4 j N

a)

the magnitude of resultant force , |F| = sqrt(5.74^2 + 19.4^2) = 20.2 N

b)

the direction of force , theta = arctan((-19.4)/5.74)

theta = 286.5 degree counterclockwise from +x axis