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

A chair of mass $12.0 \mathrm{~kg}$ is sitting on the horizontal floor; the floor is not frictionless. You push on the chair with a force $F=40.0 \mathrm{~N}$ 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 Chapter 4 number 31, we've got a chair sitting on a floor that is not frictionless.

00:05 We're pushing down on the chair at 40 newtons with an angle 37 degrees with the horizontal.

00:11 First up, we want to draw a free body diagram for the chair.

00:15 So let's go ahead and do that.

00:17 We're going to take care of the weight of the chair that's going down.

00:20 We're going to take care of the normal force on the chair going up.

00:25 And we have a frictional force going back to the left, opposing that.

00:30 At least the horizontal component of our push force.

00:33 So that's just what the free body diagram looks like for part a.

00:36 Now in part b they want us to find the magnitude of the normal force acting on the chair.

00:42 And so this is going to be a force acting in the wide direction, so we're going to use newton's second law and look at the net force in the wide direction.

00:51 That chair is not accelerating up or down, so the net force in the wide direction is zero.

00:55 So filling in the forces that we have acting in the wide direction, normal force is positive, because it's going up, the weight of the chair, mg, is going down, and we have a component of that 40 -newton force going in the negative y direction.

01:12 So that's why i made it negative.

01:14 Let's take a look at what those components actually look like.

01:17 We've got one component of that push force going horizontally, and we have one component of that push force going down.

01:25 So picking up the down arrow and completing our right triangle over here, let's draw a little bit of that push force going down.

01:30 Bit bigger picture.

01:31 We got that component...

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