A chair of mass 12.0 kg is sitting on the horizontal floor;...

A chair of mass 12.0 kg is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force $F =$ 40.0 N that is directed at an angle of 37.0$^\circ$ 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

Free-Body Diagram

A free-body diagram is a visual representation of all the forces acting on a single object. It helps in identifying and isolating each force so that their contributions can be analyzed. In mechanics problems, drawing a clear free-body diagram is essential for applying Newton's laws and understanding the interactions between the object and its environment.

Newton's Laws of Motion

Newton's laws, particularly the second law (F = ma), are fundamental to analyzing how forces affect the motion of an object. In problems like this, they allow us to set up equations based on the balance of forces in different directions, which is vital to solving for unknowns like the normal force.

Normal Force

The normal force is the perpendicular contact force exerted by a surface on an object in response to the object's weight and any additional forces acting perpendicular to the surface. It is a reactive force that prevents objects from passing through solid surfaces and plays a crucial role in determining frictional forces.

Force Decomposition

Force decomposition involves breaking a force into its horizontal and vertical components using trigonometric functions. This process is key when dealing with forces that are applied at an angle, as it enables the separate analysis of how different components of the force contribute to acceleration or equilibrium conditions.

Transcript

00:01 All right, so we have a lot going on in this problem, namely a chair with various forces acting on it.

00:10 So for simplifications, we're going to draw our chair like that, like a nice little square, and then take the forces that are being acted on it in order from easiest to least obvious.

00:23 So i think the most obvious force that is always going to be acting on the chair is the force of gravity.

00:27 That's going to be equal to the chair's mass times the excephalibious.

00:30 Due to gravity.

00:34 And in order for the chair to not go anywhere up or down, we're just sliding horizontally in this problem, there has to be some sort of vertical force to counteract the force of gravity, and this is the normal force of the floor, pushing back up on the chair.

00:50 We do also know that someone, you, are applying a diagonally downward force.

00:58 We're just going to call that f.

01:00 And we know precisely which angle you are applying that force at.

01:06 And that is going to be at theta or in this problem, 37 degrees below the horizontal.

01:14 So theta is going to be equal to 37 degrees.

01:17 And then lastly, we are told that this is not a frictionless surface.

01:22 So because the block is sliding to the right in the way that i've drawn in this problem, we will have a kinetic friction acting to oppose this motion, so that is going to be directed to the left.

01:35 So that completes our free body diagram, and that was part a of the problem, by the way.

01:40 So in part b, we are tasked with calculating the normal force.

01:45 So there are a lot of forces on this block and lots of distractions.

01:50 We tend to associate any frictional force with the normal force via...

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