consider a child who is swinging. as she reaches the lowest point in her swing: This is a topic that many people are looking for. caraimica.org is a channel providing useful information about learning, life, digital marketing and online courses …. it will help you have an overview and solid multi-faceted knowledge . Today, caraimica.org would like to introduce to you Pendulum – Tension at Lowest Point. Following along are instructions in the video below:
Guys so ive got a problem for us here. I want you to find find the tension in the rope. When the ball is at its lowest point.
So ive got a ball that i kind of wound up to here and then let it go in a pendulum motion and started swinging like this and the rope. That attached the ball to the ceiling was five meters long the ball weighed two kilograms and at its lowest point. It was going six meters per second this way and i just want to know what is the tension in the rope.
When the ball is at this point here at its lowest point. So. We know tension is just a force applied to a string or a rope and since its a force.
We know its going to be equal to mass times acceleration. So we already know the mass right we already know its two kilograms. So we can include that here.
But we dont know the acceleration right thats the tricky part you might guess that okay of course gravity is going to always be acting straight down gravitational acceleration. But theres also something else we need to account for here. And its the reason.
Why the tension isnt as high here as it is here imagine youre at a swing set at a park.
When youre sort of wound up to the to the back of the swing. And youre getting ready to swing down you feel almost weightless right here dont you. But then when you get to the bottom.
When youre at the lowest point. You feel very heavy almost as if youre being pulled down into your seat. And thats because of something called centripetal acceleration also known as radial acceleration.
And its expressed with velocity squared over radius of the circle that youre moving in in this case. We have a partial circle centripetal acceleration. Applies whenever youre moving in a circle.
Or a partial circle. The example. I like to use is a roller coaster so when you get to the bottom of a roller coaster loop.
You feel very heavy in your seat. Just like on that swing set and thats because not only is gravity pulling you down. But something called centripetal acceleration is also pulling you straight down because centripetal acceleration.
Always acts directly out of a circle.
And when you get to the top of a roller coaster loop. You feel nearly weightless and this is because again gravity is acting straight down. But this time centripetal accelerator is acting straight up because its it always acts directly out of the circle and at this point.
Centripetal acceleration and gravity oppose each other they almost cancel each other out. And thats why you feel weightless you know if this roller coaster were to stop right here. You would have no more eccentric acceleration.
Because you would no longer be moving in a circle gravity would take over and unless you were properly secured in your seat. You could fall out thats why centripetal acceleration is so important in the calculation. And the engineering of making a roller coaster so back to our problem.
We know were moving in sort of a partial circle here like this right so centripetal acceleration. At this point is going to be acting straight out of that circle right so ill abbreviate centripetal acceleration c. A.
So now we know for our acceleration. We actually have to add together gravity and centripetal acceleration to account for this so. Gravity we know is always going to be 98 meters per second squared.
But centripetal acceleration.
We have to calculate with this expression velocity squared over radius of the circle or partial circle. So we know velocity is 6 meters per second right so well have 6 squared over the radius of this partial. Circle which is 5 right so our gravity is 98.
And our centripetal acceleration is 36 over 5. So now we can add those in to our acceleration. Variable.
Here so ill add together 98. Meters per second squared plus 36. Over 5 meters per second squared.
These are both in units of meters per second squared or acceleration. And when you multiply those out on your calculator. You should get 34.
And this is in units of newtons because it is a force so i hope that made sense. If you guys are interested in any tutoring or have any questions please contact me at facebookcom. De novo tutoring.
Ill see you guys in the next video thanks a lot .
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