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## Physics library

### Course: Physics library>Unit 3

Lesson 7: Treating systems

# Treating systems (the hard way)

Created by David SantoPietro.

## Want to join the conversation?

• At how can you take the acceleration of the (3kg) body to be downwards?? (5kg) has greater mass than (3kg) so there would not be any acceleration in the downward direction the masses will just hang in there without any movement!
• While that might seem to be the case, that is actually incorrect for this situation. The force of gravity is pulling down on the 3kg block. That force is then transferred through the rope and is applied to the 5kg block. This force is acting upon the 5kg block in the horizontal direction, and since there is no friction on the table, it is the only force acting on the 5kg block in the horizontal direction. This will cause there to be a net force on the 5kg block in the horizontal direction, which will cause it to accelerate to the right.
• I dint get why the acelerations have oposite signs in .
Vectors with oposite signs means oposite directions and thats not the case
• This comes about as a result of 2 things:

1. The way he has defined his coordinate system; and
2. The way pulleys work

First of all, he has defined motion in the upwards direction to be positive (thus downwards motion is negative), and motion in the rightwards direction to also be positive (thus leftwards motion is negative). This is pretty standard convention when teaching and learning elementary physics, but really, as long as you're consistent, you can choose which direction is positive and negative.

Secondly, there's the way pulleys work. As you can see from the way the picture is drawn, if the mass on the table (the 5kg mass) was to move leftwards, it would actually pull the 3kg mass up. Likewise, if the 5kg mass were moved to the right, the 3kg mass would have to move down. Remember from point 1 (above) that upwards and rightwards motion is positive, whilst leftwards and downwards motion is negative. So to rephrase what I just wrote, if the 5kg mass were moved to the right (positive), the 3kg mass would have to move down (negative). To reiterate what was already said in the video, the pulley will translate horizontal motion into vertical, and vice versa.
• since there is no friction nor air ressistence the mass on the table could be 10000kg and the acceleration would still be the same, right?

And why did we assume that we had an acceleration?
• If you have something floating in space, the fact that it's floating in space doesn't mean you need no force to move it, only that the force you need to move it is less than in circumstances when you have other forces interfering. In this case the force of friction is negligible but there is still a tension between the two boxes that is pulling the 3kg box upwards. If i'm not mistaken, the magnitude of the force of tension depends on the masses of both boxes and, if you think about it, if the box on the table was say 100 grams, it would accelerate a lot faster. It makes sense that the opposite is also true. Anyway, you can calculate for a box of 10000kg if you want with the ecuation he used almost at the end: 29.4N=(5kg)(a5x)+(3kg)(a5x) you replace the 5kg with 1000kg and you get a5x=29.4/1003=0.03m*s^-2 So you can see that, no matterwhat the mass of the box on the table is, because it has no friction it will allways accelerate, but not allways at the same rate: as it becomes bigger the acceleration will aproach 0 but never reach it. That's why we asume that there is an acceleration.
• Should not the tension equal the weight of the 3kg since there is no friction?
(The 5kg should not even be able to hold the 3kg since no force of friction or any force is in the -x directions of the 5kg. So there is no tension force pulling up the 3kg. Right?)
Also there should not be any upward tension for the 3kg box, (since nothing is pulling it up) right?
• If we assume T up at 3kg box is 30N, so a=0 for the 3kg box.
So T pulling the 5 kg box will be 30N, thus a= F/m=6ms-2
The magnitude of acceleration at two boxes is different! If this happens, tension will not retain, so in this situation, this can't happen!
From the video, the assumption made is that the magnitude of acceleration of two boxes are the same so tension will keep constant
• Shouldn't the acceleration just be 9.81m/s since there is no friction and thus there is no force that is acting against the weight? I thought tension would not exist in this case because the 5kg block is not creating any force against the rope?
• You are forgetting about inertia. To move the 5 kg block, the rope has to pull on it, even in the absence of friction. Remember how Newton's first law tells us that a body at rest will remain at rest as long as there is no net force acting on it? Also, the tension results because there is another block of mass 3 kg attached at the other end of the rope and pulling on it.
As the rope pulls on the 5 kg block, the block pulls back on the rope with an equal amount of force and in the opposite direction. Similarly, the 3 kg block is being pulled up by the rope while gravity is pulling it down. So the 3 kg block is not in free fall and therefore it's acceleration will be less than 9.81 m/s^2.
If there were friction, the acceleration would have been even smaller!
• Shouldn't the 5kg mass not move as it is heavier than the other mass (3kg)?

• Since there is no friction between the table and the 5kg mass, it will move wherever a force pushes or pulls it. The acceleration on the 3kg mass accelerates the 3kg mass down, which pulls the rope, which pulls on the 5kg mass (to the right).
• wait, wouldn't it be incorrect to assume that the acceleration of the two objects are equal like David did at , because those two objects have different masses, and thus it cant be the same acceleration!
• The two masses are bound together by the string, which means that the 3kg box will pull the 5kg box, and the 5kg box will slow the 3kg box so that they both accelerate the same. The weight force on the 3kg box provides the acceleration for the total system.
• Would't the forces be different because of different mass? I.e he says that T is the same for both the 5kg box and the 3kg box.

But with both boxes having the same Acceleration= 3,68m/s^2. The forces will be different by Newtons 2. law.
F5x = m5* a5x -> F5x = 5* 3,68 = 18,4N.
F3y = m3* a3y -> F3y = 3* 3,68 = 11N

So how can T- tension be the same when the forces exerted is different because of mass!?
• This same thing is true if you pull 2 objects of different masses in a straight line. How would the force of tension be multiplied along a straight piece of string?
It helps if you see the next video and understand both objects as part of one system:
Force of tension on 5kg object(and 3 kg object as we will see):
5*3.675=18.375newtons
Force on both objects due to gravity and gravity acting through tension in the rope:
3*9.8=29.4newtons
Tension on the 3kg object
29.4-(3*3.675)=18.375newtons of tension
The total force available for acceleration is only 3kg*gravity or 29.4N. Because acceleration is only 3.675m/s^2 the remaining force is being absorbed by tension. Otherwise we would see the 3kg have a larger acceleration and deliver more force on impact with the ground.