The energy accumulated in the construction is about 2-3 Joules. In this first video we ask the question "How can we keep the energy in the system". How many Joules of energy should we input from the motor in order to keep the energy in the system.
- # 119
- 10 Dec 2015
We would introduce Force and Power as values. We would use a scale to do the measurements. We measure the force of weight and from there we would calculate the Power.
Previous video tutorials:
- Physics in LEGO Mindstorms: Energy Accumulation and Conservation. Part 1
Previously we built this construction and we did a few experiments and calculations on how much energy we can accumulate in this construction with these 3 wheels that is powered with this motor. For example, when we start the program. Let me just start the program. And what you can see is that the wheels rotate quite fast. This will continue for about 10-15 seconds. And in the end they will stop at their maximum speed.
The energy that is accumulated in this construction is about 2, 3 joules. And we finished off with exactly what we do with so much energy and can we convert it, can we use this energy for something, what does it mean to have 2 or 3 joules of energy.
So let's first talk about the following question that we'll experiment with in the next 1 or 2 videos.
How do we keep this energy in the construction? How much energy do we need from the motor in order to keep the wheels rotating?
There are several possibilities. We can have 3 joules of energy here we must input 3 joules from here, or we can input 1 joule, or 5 joules how many joules of energy do we input from the motor so that we can continue rotating the wheels. In order to calculate this we'll use a device like this. Something that can measure the weight.
We'll introduce one more value. It's the force and then we'll introduce power. Just a very brief introduction and we'll try to find how much energy do we input from the motor in order to keep the wheels rotating.
First thing you should know is that it takes some time for the wheels to reach maximum speed of rotation, maximum angular velocity and we can measure using this scale, we can measure the force that is exerted from the motor. With this force we can actually calculate the power and from there the energy that is input from the motor to the system. For this we'll use this scale. Let me just turn it so that you can see it more clearly. Now this is scale that measures kilograms and on the little display you'll see the grams. Now it's about 0 grams.
At the beginning you'll see that we need much power in order to start rotating the wheel because these are acting like flywheels and we need more power. And after 15 seconds or so we'll reach a stable value and you can see that the force from the motor to the scale is always the same.
As a result of this experiment we can conclude that after about 15 seconds the force from the motor to the scale is equal to about a 100gr. (0,1kg.).
How do we convert from the mass to power, to force?
This is something that we'll do now on the computer. But you saw that it was 93-94 for easier calculations we can use a 100 because it's easier to calculate this. Let's see how much energy do we input from the motor into the system. Here are the calculations. In the previous video we did a calculation on the energy that was accumulated, so we reached about 2 joules and it was dependent on the speed of rotation of the motor. If we have a speed of about 8 radians it is 2 joules, if we have speed of 12 radians it's about 5 joules. And it depends on the different motors, the battery level, etc. So this is the output power. That's the power that is accumulated. But how much energy do we add into the system? We measured the wight in kilograms, and the wight that we measured, that's the mass, was about 0,1 kg. We are working in a system international so all the measurements are in the standard units and 0,1kg. is a 100gr. as the scale showed. So we need the force, that is exerted from the motor to the scale, the force. It is very easy to calculate. It is actually the mass. So it's C12 multiplied by the earth gravitational acceleration, that is 9,81. And this here is in Newtons. Then we need, if you find it too for the formulas, don't mind the formulas I'll just follow them so that we can reach to some conclusion what is the power that we add into the system.
So we have force, from the mass we find the force and from the force we'll find the moment. The moment that we add to the system and it's actually the force C13 multiplied by the length of the motor, because there's some length from the place where the motor is connected to the construction to the place where the motor touched the scale and that's acting like a lever and we know the force and we know the length and the length is about 0,08 meters so the torque in Newton meters is about 0,07 and from then we can actually find the power. The power is equal to omega so that's the angular velocity multiplied by the moment. And we have the moment and the angular velocity. The angular velocity of the motor is about 12 radians and the moment is about 0,07. Let's multiply this. It's C14 multiplied by 12 and that's in Watts.
So this here are the units. We have the mass, the force, the moment and the power.
The power is 0,94 W or approximately a Watt per second. This means that our system, when the motor is rotating and the whole construction is rotating our motor is adding 1W each second to the system, which is actually 1 joule, because a joule, the energy that we add is actually a Watt, Watt per second.
Now we'll have the formulas below, again, I don't want to go into much details to make it very difficult.
The goal here is to find the power and the power is about 1 Watt per second.
And what do we have? We have a system, where we have 2 energies The energy that is accumulated in the system is about 5 joules and the energy that we add to the system each second is about 1 joule. So it's actually C15 multiplied by 1, because this is per second. And this tells us something. This tells us that we have energy. We have this energy accumulated and after 15, 16, 17 second when the whole system is stable we can keep this energy accumulated by adding only 1 joule in this system, 1 Watt per second.
So we can keep 5 joules by using only 1 joule and we can keep this 5 joules for a later moment, something that we'll show in one of the next videos.