A. What is F ? b. What is the tension at the top end of rope...

Key Concepts

Force Equilibrium

This concept refers to the condition in which the sum of all forces and moments acting on an object or system is zero. In static problems, such as one involving ropes under tension, it’s essential to set up equilibrium equations to ensure that forces balance in every direction, allowing for the determination of unknown forces or tensions.

Tension in Ropes

Tension is the pulling force transmitted along a rope, cable, or string when forces are applied at its ends. In idealized scenarios where the rope is assumed to be massless and inextensible, the tension is constant throughout its length, making it a key factor when analyzing forces in rope-pulley systems.

Free Body Diagrams

A free body diagram is a schematic representation of an object or a system that isolates it from its surroundings and shows all external forces acting upon it. This tool is critical for visualizing and setting up the equations required to solve for unknown quantities like the tensions in different segments of a rope.

Pulley Systems

Pulley systems are arrangements of wheels and ropes used to change the direction of an applied force and potentially gain a mechanical advantage. Understanding how forces are distributed throughout a pulley system, and how tensions differ in various segments of the rope, is fundamental to solving problems involving multiple ropes or changing points of force application.

Transcript

00:01 In this question, we have a system of two blocks, a and b, both are same mass of 1kg.

00:09 They are connected by two ropes, which is r1 and r2, in which both of them are not massless.

00:16 The ropes have mass of 0 .25 kilograms or 250 grams.

00:21 We are given that the system is accelerated upwards by a force with an acceleration of 3 meters per second square.

00:31 I want to find what is the force f.

00:34 So very simple, we draw the free body diagram of the system.

00:40 So let us consider the system as the entire square over here.

00:45 There is force f that's acting on it, and then there is gravity.

00:51 The net force would cause an acceleration of 3 meters per second square.

00:56 So there is the total mass times 3 mt per second square.

01:02 And the net force is given as f minus fg and the total mass over here will be the mass of the two blocks which is two kilograms plus the mass of the ropes which is 0 .5 kilograms so there is 2 .5 times 3 taking the force of gravity to the right hand side right fg is equal to total mass again multiplied by 9 .8 1 due to gravity.

01:37 So we should get our f to be equivalent to 32 neutered after bringing the force of gravity over.

01:49 Now we want to find what is the tension at the top half of our rope.

01:56 So to do that we're going to consider the free -boli diagram of our block a.

02:01 So block a experiences a force coming from the top.

02:06 Which is f which is equals to 32 newtons it experiences gravity right fg from itself and it experiences the tension coming from the rope one from the top half of r1 so now we can find what is the tension by knowing what is our force of gravity here and that the net force acting on a, f -net, must be equal to the mass of a multiplied by the common acceleration, which is 3 meter per second square.

03:02 So this is equal to 32 minus the force of gravity minus the tension from the top half of rope 1.

03:18 Rearranging this equation should get the tension from the top of r1 to be equals to 19 .2 newtons you just have to substitute the values in this is 3 this is 1 kilograms this is 1 this is 9 .81 this is the top half now to consider the bottom half now if you consider the bottom end the bottom the end of the rope...

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