Please help me understand this? Connected Objects

  • Thread starter CVRIV
  • Start date
In summary, the book says that a2=-a1, but when the author tried to solve the problem using this equation, it didn't work. He realized that he had to be consistent and inverting the polarity of m1a2 from the start.
  • #1
CVRIV
12
5
I attached an image of the problem and solution from the book and my attempt at solving it. I don't need help solving the problem the way the book explains it; i understand that.

What I don't understand is why I can't solve for (a2) instead of (a1). The book says a2 = -a1, which makes sense to me, because the magnitudes are the same except the polarity for a2 is negative.

What about a1 = -a2? I tried solving the problem the same way except I substituted -a2 for a1 instead of the other way around and it doesn't work. I just don't understand why it wouldn't work.

Please help me understand this.
 

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  • #2
You need to keep the signs consistent. In your first equation a positive a1 means the mass accelerates towards the edge. In your second equation a positive a2 means the mass accelerates downwards. That is possible - but then you have a1=a2 without the minus sign.
 
  • #3
Why would positive a2 accelerate downwards? I thought positive a2 accelerates upwards?

In equation 2 I divided both sides by -1 so that I could cancel out the tension T. Was that not right?
 
  • #4
Oh wow. I think I know what I did wrong. How stupid of me. :confused:
 
  • #5
CVRIV said:
Why would positive a2 accelerate downwards? I thought positive a2 accelerates upwards?
It is arbitrary which direction you choose, but you have to be consistent.
 
  • #6
Finally! The problem was that from the very start I was inverting the polarity of m1a2. I kept writing down T - m2g = -m2a2. I did that because I had it in my head that a2 was negative, which it is, but only after solving for a2. By assigning it as negative from the start, I was in fact just screw it all up. Also... I had it stuck in my head that I had to add the two equations together. I went back to the previous problem in the book, which as a Atwood's Machine problem, and it was subtracting the equations. I I thought I was doing it wrong so I told myself I have to subtract the problems. That's when I realized, fully realized, that it totally depended on the cancellation of T. I get it now. Thanks for your help.
 

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What are connected objects and how do they work?

Connected objects, also known as Internet of Things (IoT) devices, are physical objects embedded with sensors, software, and network connectivity that allow them to collect and exchange data with other devices and systems. They work by connecting to the internet or other networks, allowing them to communicate and share data with other devices or systems.

What are the benefits of using connected objects?

Connected objects offer numerous benefits, such as increased efficiency, improved data collection and analysis, enhanced automation, and better decision-making. They can also improve communication and collaboration between different devices and systems, leading to a more interconnected and streamlined environment.

What are the potential risks or challenges of using connected objects?

One of the main risks of using connected objects is cybersecurity threats, as these devices are vulnerable to hacking and data breaches. Other challenges include compatibility issues with different devices, data privacy concerns, and the potential for technological malfunctions or failures.

What industries are currently utilizing connected objects?

Many industries are currently utilizing connected objects, including healthcare, transportation, manufacturing, agriculture, and smart homes. These devices are being used for various purposes, such as remote patient monitoring, smart energy management, inventory tracking, and precision farming.

How is data collected and used from connected objects?

Data from connected objects is collected through sensors, which can measure and record various data points such as temperature, humidity, motion, and location. This data is then transmitted to a central system or the cloud, where it can be analyzed and used to make decisions or trigger actions. The data collected can also be used for predictive maintenance, performance optimization, and other applications.

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