Question

Three forces act on an object, with force F2 acting in the positive x direction. (a) Find the magnitude of the net force acting on the object? (b) Find the direction of the net force. The angle is measured from the positive x axis. (c) Find the fourth force that a person would have to exert on the object to make the net force equal to zero.

F1=11.0N at an angle of 40 degrees above the horizontal

F2=12.0N

F3=10.0N along the -y axis

Answer 1

(a) The components of the first force are

The first force vector is

The second force points along the positive x-direction, the second force vector is

The third force points along the negative y-direction, the third force vector is

The net force is the vector sum of these three forces

The magnitude of the net force is

(b)

The x-component of the net force is positive, the net force points to the right. The y-component of the the net force is negative, it points below the x-axis as shown in the above figure. The angle that it makes with the x-axis is

where the negative sign represents that the direction is below the horizontal.

(c) In order to balance the force we need to apply a force of same magnitue but in the opposite direction, as shown in the following figure:

The fourth force makes with the net force. The angle that it makes with the positive x-direction is

The magnitude is the same as the magnitude of the net force.