Question

A force has a magnitude of 10 N, and it is forming and angle of 30o with an x-axis. Find xand y-components of this force.

2. Calculate the magnitude and direction of a force if its x- and y-components are specified: Fx = 0.832 N, Fy = - 1.455 N.

3. In 2D Cartesian coordinates, a force F has the following components: Fx = - 5.0 N, Fy = 8.0 N. Find the magnitude and direction of the force.

4. A force of 5.0 N is applied to a point object at 30o with the horizontal. Another force of 10.0 N is applied at 120o . a) Determine the net force (the magnitude and angle). b) What force (magnitude and angle) has to be applied to the same object to restore the equilibrium (to obtain zero net force)?

Answer 1

1))

Fx = F*cos30 = 10*0.866 = 8.66 N

Fy = F*sin30 = 10*0.5 = 5 N

2)

magnitude F = sqrt(Fx^2 + Fy^2) = sqrt(0.832^2 + 1.455^2) = 1.676 N

direction = theta = arctan(-1.455/0.832) = 360 - 60.23 = 299.77 degree counterclock wise from +x axis

3)

magnitude F = sqrt(Fx^2 + Fy^2) = sqrt(5^2 + 8^2) = 9.43 N

direction = theta = arctan(8/(-5)) = 180 - 60= 120 degree counterclock wise from +x axis

4)

F1 = 5*cos30 i + 5*sin30 j = ( 4.33 i + 2.5 j ) N

F2 = 10*cos120 i + 10*sin120 j = ( - 5 i + 8.66 j ) N

a)

F = F1 + F2 = (4.33 - 5)i + (2.5+8.66) = - 0.67 i + 11.16 j N

magnitude = sqrt(0.67^2 + 11.16^2) = 11.18 N

theta = arctan(11.16/(-0.67)) = 180 - 86.56 = 93.44 degree

b)

F = - (F1 + F2) = 0.67 i - 11.16 j N

magnitude = 11.18 N

theta = arctan(-11.16/(0.67)) = 360 - 86.56 = 273.44 degree