What is the resultant of the forces F1 and F2 acting on the cart, what can you say about the movement of the cart?

To answer this question, it is necessary to draw some conclusions from the problem statement:

The direction of these forces;
Modular value of forces F1 and F2;
Can these forces create such a resultant force to move the cart.

Direction of forces
In order to determine the main characteristics of the movement of the trolley, which is under the influence of two forces, it is necessary to know their direction. For example, if the cart is pulled to the right by a force equal to 5 N and the same force is pulling the cart to the left, then it is logical to assume that the cart will stand still. If the forces are co-directed, to find the resulting force, it is only necessary to find their sum. If any force is directed at an angle to the plane of movement of the trolley, then the value of this force must be multiplied by the cosine of the angle between the direction of action of the force and the plane. Mathematically, it will look like this:

F = F1 * cosa; where

F – force directed parallel to the movement surface.

Cosine theorem for finding the resulting vector of forces
If two forces have their origin at one point and there is a certain angle between their direction, then it is necessary to complete the triangle with the resulting vector (that is, the one that connects the ends of the vectors F1 and F2). We find the resulting force using the cosine theorem, which says that the square of any side of a triangle is equal to the sum of the squares of the other two sides of the triangle minus twice the product of these sides by the cosine of the angle between them. Let’s write it in mathematical form:

F = F1 ^ 2 + F2 ^ 2 – 2 * F1 * F2 * cosa.

Substituting all known values, you can determine the magnitude of the resulting force.