A chair of mass 13.5 kg is sitting on the horizontal floor;...

A chair of mass $13.5 \mathrm{~kg}$ is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force $F=35.0 \mathrm{~N}$ that is directed at an angle of $38.0^{\circ}$ below the horizontal, and the chair slides along the floor. (a) Draw a clearly labeled free-body diagram for the chair. (b) Use your diagram and Newton's laws to calculate the normal force that the floor exerts on the chair.

Key Concepts

Newton's Laws of Motion

Newton's laws, especially the second law, state that the net force acting on an object is equal to the mass of the object multiplied by its acceleration. In problems involving equilibrium, the sum of the forces in each perpendicular direction must be zero. This principle is used to balance forces, such as the weight and the vertical component of the applied force, to determine other reaction forces.

Free-Body Diagram

A free-body diagram is a simple sketch that represents all the forces acting on an object. It helps in visualizing the forces such as weight, normal force, friction, and any applied forces, and shows their directions and relative magnitudes. This graphical tool is essential for setting up the equations of motion using Newton's laws.

Force Decomposition

Force decomposition involves breaking down a force applied at an angle into its horizontal and vertical components. This process, typically using sine and cosine functions, allows one to analyze the effects of the force in different directions, which is crucial when applying the conditions of equilibrium or calculating net forces.

Normal Force Calculation

The normal force is the reactive force exerted by a surface, acting perpendicular to it, to prevent an object from accelerating through the surface. Calculating the normal force involves setting the sum of the vertical forces to zero when there is no vertical acceleration, thereby balancing the object's weight against the vertical component of any applied force.

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