A force F is applied to each of two ropes (of negligible...

A force $\mathrm{F}$ is applied to each of two ropes (of negligible weight) attached to opposite ends of a 40 -kg wagon and making an angle of $35^{\circ}$ with the horizontal (Figure 16$)$ . What is the maximum magnitude of $F($ in newtons) that can be applied without lifting the wagon off the ground?

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Key Concepts

Free-Body Diagram

A free-body diagram is a simplified representation of an object that illustrates all the external forces acting on it. This tool is essential for visualizing and analyzing the forces involved in a problem by isolating the object and showing forces as vectors, helping to systematically apply the laws of motion and equilibrium.

Force Decomposition

Force decomposition involves breaking a force vector into its components, typically along mutually perpendicular axes such as horizontal and vertical. This technique is crucial for solving problems because it allows the analysis of the effects of each component separately, using trigonometric functions like sine and cosine.

Equilibrium of Forces

The principle of equilibrium states that the sum of all forces acting on an object must be zero if the object is at rest or moves with constant velocity. This condition is applied separately in each directional axis (e.g., vertical and horizontal), ensuring that the net force in each direction is balanced.

Gravitational Force

Gravitational force is the force with which the earth attracts an object towards its center. This force is normally represented by the weight of the object in problems and must be balanced by other forces (such as vertical components of applied forces) to prevent vertical acceleration.

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