IE . co Two blocks are connected by a light string and...

IE . co Two blocks are connected by a light string and accelerated upward by a pulling force $F$. The mass of the upper block is $50.0 \mathrm{~kg}$ and that of the lower block is $100 \mathrm{~kg}$. The upward acceleration of the system as a whole is $1.50 \mathrm{~m} / \mathrm{s}^{2} .$ Neglect the mass of the string. (a) Draw the free-body diagram of each block. Use the diagrams to determine which of the following is true for the magnitude of the string tension $T$ compared to other forces: $(1) T>w_{2}$ and $T<F ;(2) T>w_{2}$ and $T>F ;$ (3) $T<w_{2}$ and $T<F ;$ or $(4) T=w_{2}$ and $T<F ?$ (b) Apply Newton's laws to find the required pull, $F$. (c) Find the tension in the string, $T$.

IE . co Two blocks are connected by a light string and accelerated upward by a pulling force $F$. The mass of the upper block is $50.0 \mathrm{~kg}$ and that of the lower block is $100 \mathrm{~kg}$. The upward acceleration of the system as a whole is $1.50 \mathrm{~m} / \mathrm{s}^{2} .$ Neglect the mass of the string.
(a) Draw the free-body diagram of each block. Use the diagrams to determine which of the following is true for the magnitude of the string tension $T$ compared to other forces: $(1) T>w_{2}$ and $T<F ;(2) T>w_{2}$ and $T>F ;$ (3) $T<w_{2}$ and $T<F ;$ or $(4) T=w_{2}$ and $T<F ?$
(b) Apply Newton's laws to find the required pull, $F$.
(c) Find the tension in the string, $T$.

Key Concepts

System Analysis

System analysis involves treating multiple connected objects as a single entity to simplify the application of Newton's Second Law. This approach helps to determine overall forces and accelerations before breaking down the analysis to study individual forces, such as tension and weight, on each object.

Gravitational Force

Gravitational force is the weight of an object, calculated as the product of its mass and the acceleration due to gravity (g). This force acts downward and is a critical component when analyzing systems that involve vertical motion or acceleration.

Tension in a String

Tension refers to the force transmitted through a string, rope, or cable when forces are applied at its ends. In problems involving connected objects, the tension is a key unknown that links the dynamics of the two objects, and it must be handled carefully, especially when the string is considered light or massless.

Free-Body Diagram

A free-body diagram is a schematic that depicts all of the forces acting on a single object. It helps in clearly visualizing gravitational forces, applied forces, and internal forces such as tension, which is crucial for correctly applying Newton's Second Law.

Newton's Second Law

Newton's Second Law states that the net force acting on an object is equal to the mass of the object multiplied by its acceleration (F = ma). This law is fundamental in dynamics as it allows us to set up equations for the forces acting on individual objects or systems when they are accelerating.

Transcript

00:01 Let's say we have two blocks.

00:03 I'll call this block mass 1 and another block mass 2 that are connected by a string and they're being pulled upward by a force f.

00:18 Let mass 1 be equal to 50 kilograms and mass 2 be equal to 100 kilograms.

00:29 And thanks to this force, we have an extent.

00:32 Acceleration of 1 .5 meters per second squared.

00:38 Let's look at a few things here.

00:40 First, let's look at the free body diagrams.

00:45 For first, let's look at the easy one.

00:48 Let's look at mass two.

00:51 If i look at mass two, what i know it's act on it is gravitational force.

00:58 I'm going to put a two to say it's gravitational force of mass 2 and tension.

01:06 And then if i solve on mutant's second law, the net force on mass 2, and let's call up the positive direction.

01:18 It's going to be t minus fg2 equals mass times acceleration.

01:30 And for now, oh, let me put t2 here as well.

01:36 For now, i'll pause that.

01:38 And then let's look at mass number one.

01:42 Mass number one feels its gravitational force pointing downward.

01:51 So i'll call it g1.

01:55 It also feels that same tension, right, in the rope pointing downward.

02:05 And also, it's going to feel a second tension force, but really that force force, f pointing upwards.

02:17 So i write out the equations and motion here.

02:22 F net a mass 1 is going to be equal to we have that force minus tension minus fg1 equals ma and we label this 2 and 1.

02:40 So that's what our free body diagram say.

02:44 And i suppose since this is the same oh, since i'm doing this from mass 1, i'll call this t1 and t1.

02:51 But because the ropes are connected, we can just go ahead and say that t2 and t1 are equal, just being t.

03:00 I also label these equations 1 and 2 and rewrite them again.

03:04 So equation 1, we have t2 minus this.

03:09 All right, i'm going to put w2 to say the weight of mass 2 equals mass 2 times acceleration.

03:18 And then we have two, equation two, oh, let me take care of this here.

03:26 Since we decided, t is the same for both mass one and mass two.

03:30 And then for equation two, i'll rewrite that as f minus t minus the weight of mass one times mass 1.

03:41 All right, so let's look at a couple things.

03:46 All right, so first, let's check this out.

03:49 So with this equation one over here, it's a couple of things...

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