Three sleds are being pulled horizontally on frictionless...

Three sleds are being pulled horizontally on frictionless horizontal ice using horizontal ropes (Fig. 5.50 ). The pull is horizontal and of magnitude 125 $\mathrm{N}$ . Find (a) the acceleration of the system and $(6)$ the tension in ropes $A$ and $B .$
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Key Concepts

Newton's Second Law of Motion

This law states that the net force acting on an object is equal to the product of its mass and acceleration (F = ma). It is the fundamental principle that connects the net force, mass, and acceleration of a system and is used to determine how an external force causes a system to move.

Combined Mass System Analysis

When multiple objects are connected and move together, they can be treated as a single system with a combined mass. This approach simplifies the analysis by using the total mass in Newton's Second Law to calculate the overall acceleration of the system under the influence of the net external force.

Internal Forces and Tension in Connecting Ropes

In a system of connected objects, the tension in each connecting rope is an internal force that varies depending on the masses it is directly accelerating. Analyzing the forces acting on individual parts of the system allows us to determine the tension in each rope by considering the net force required to accelerate the remaining masses attached to that rope.

Free-Body Diagrams

Drawing free-body diagrams is a crucial technique in physics to visualize and analyze all the forces acting on each object in a system. They help in isolating each component of the problem, making it easier to apply Newton's Second Law to determine acceleration and tension forces in connected bodies.

Transcript

00:01 Okay, so the first question was asking us, what is the acceleration of the system? well, so the system was made up with three slas and the ropes, okay? and each slats has different weights, which means have different mass, okay? so since we need to consider three slats as a whole system, so the mass of a system is the total mass of the three slats.

00:34 And we know the force was given as 125 newtons.

00:38 And we know such formula which is f equal to ma.

00:42 Okay? so a is equal to f over the total mass.

00:50 And total mass is equal to m1 plus m2 plus m3.

00:53 So f over m1 plus m2 plus m3.

01:04 And this will give us a is equal to, so a is equal to f, which is the 4 ,000, which is given as 125 newtoms.

01:25 Oh, what am i doing? over m1 which is 30 kilograms plus m2 which is 20 kilograms and m3 is 10 kilograms and this will give us that the acceleration is equal to it's about 2 .08 meter per second square and for question b he was asking us, what is the tension on row a and b? so looking for tension on row a and b.

02:47 So tension on row a is just equal to the net force on the it's just equal to the net force on the row a, okay? so f -nat -a is equal to t -a.

03:19 This can be equal to m1 plus m2 because rope a was pulling the bow one and bow two, i'm sorry, the sled one and slat two, and times the accelerations, okay? so we get ta is equal to m1, which is 30 kilogram, plus m2 is 20 kilograms times the acceleration was given as 2 .08 meter per seconds...

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