The drawing shows box 1 resting on a table, with box 2...

The drawing shows box 1 resting on a table, with box 2 resting on top of box 1. A massless rope passes over a massless, frictionless pulley. One end of the rope is connected to box 2, and the other end is connected to box 3. The weights of the three boxes are $W_{1}=55 \mathrm{N}, W_{2}=35 \mathrm{N}$ and $W_{3}=28 \mathrm{N}$ . Determine the magnitude of the normal force that the table exerts on box 1 .

Key Concepts

Tension in Ropes and Pulleys

In systems with ropes and pulleys, tension is the force transmitted along the rope, assumed to be uniform in ideal systems with massless ropes and frictionless pulleys. This concept allows the forces to be connected across different objects in the system, enabling a consistent analysis of their interactions.

Static Equilibrium

Static equilibrium refers to a state where an object or system experiences no net force and no net torque, meaning it remains at rest. This concept is crucial for analyzing problems where multiple forces, including gravitational, normal, and tension forces, must collectively cancel out for the system to remain stationary.

Newton's Laws of Motion

Newton's laws of motion, particularly the first (law of inertia) and second (F=ma), provide the framework for analyzing forces and the resulting accelerations or equilibrium conditions. In problems involving static contacts and pulleys, these laws are fundamental to setting up balance equations for forces.

Free-Body Diagram

A free-body diagram is a graphical illustration used to visualize all the forces acting on a single object in a system. It simplifies the analysis by isolating the object and representing forces such as weight, normal force, tension, and friction, facilitating the application of Newton's laws.

Normal Force

The normal force is the reactive force exerted by a surface to support the weight of an object resting on it. It acts perpendicular to the surface and adjusts to balance the net force acting in the perpendicular direction, ensuring that the object does not accelerate through the surface.

Transcript

00:01 In this question, the following forces are in action.

00:03 We have the weight force of the box number one, which acts on the box number one itself and on the ground.

00:10 Then, the ground acts on box number one by a normal force, which i had called n1.

00:17 The second box has also its weight force, w2, acting on it, but it also acts on box number one with its weight force.

00:26 And because of that, the box number two receives a non -year -two.

00:30 Force called the normal force n2 which is the force that is exerted by the box number one on the box number two as a response to the weight of box number two then the box number two is also pulling down this rope with some force that i had called f and as an answer to that force f the rope pulls the box number two up and with a with a force that i had called t that force t is also present here and it is reacting to another force f which is equal to the force w3 which is the weight force of the turned box then in blue are the forces that are exerted by the boxes and in red there are the forces that are exerted on the boxes we want to calculate what is the value of the normal force that the table exerts on box 1 so we want to calculate and 1 how can you do that? well, by applying newton's second law in this direction, which is the vertical direction, let me call it y.

01:39 Then we have to apply newton's second law, probably to several objects in this situation.

01:46 So the force we are interested, the force n1, is acting on box number one.

01:51 So let us apply newton's second law to box number one.

01:55 So on box number one, the net force on the y direction, but as it is the only direction, of interest in this problem, i will not be writing fn component y or anything like that.

02:09 So the net force in the interesting direction is equal to the mass of box number one times its acceleration in that direction.

02:19 But note that the box number one is standing still, so its acceleration is equal to zero.

02:24 Then the net force that acts on box number one is equal to zero...

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