On a body weighing 3 kg, two different forces are directed at an angle of 60 degrees to each other.

On a body weighing 3 kg, two different forces are directed at an angle of 60 degrees to each other. With what acceleration does the body move if the moduli of forces are 9 N?

Given:

m = 3 kilograms – body weight;

F1 = F2 = F = 9 Newton – modules of forces acting on the body;

y = 60 degrees is the angle between the directions of forces.

It is required to determine the acceleration of the body a (m / s ^ 2).

Let us find the projection of the forces acting on the body onto the X axis:

F1 = F2 = F * cos (y / 2).

Then the resultant forces will be equal to:

F3 = F1 + F2 = F * cos (y / 2) + F * cos (y / 2) = 2 * F * cos (y / 2).

The acceleration of the body will be equal to:

a = F3 / m = 2 * F * cos (y / 2) / m = 2 * 9 * cos (60/2) / 3 =

= 18 * cos (30) / 3 = 6 * cos (30) = 6 * 0.87 = 5.2 m / s ^ 2.

Answer: the acceleration of the body is 5.2 m / s ^ 2.