Hello everyone. I am creating a SERIES of note walls for my profile, where every solution I did to problems in Brilliant were correctly done but mismanaged to get the right answer. In other words, I DID NOT TRUST MY GUTS AND I F&@KED UP!!! (Sorry about the language.) Because of this, I am not be able to post my solutions to the problem and I can no longer share my approach but otherwise, do them here.
On this first episode, I want to share my solution to 3/11/2021 Daily Challenge—Friction on Friction.
So, to sum up the question from the daily challenge, what happens to the frictional force of the top book that is piled upon another book when both of their accelerations are doubled?
Here is my mathematical approach of the problem:
Newton's 2nd law of motion, Law of Acceleration, states that the acceleration of the books times their mass is equal to the sum of their net forces. So by plugging in the formula,
we will derived at the following solution:
From the set of equations above, it means that when the acceleration DOUBLES, the frictional force of the books also DOUBLES.
Here concludes one of those frustrating days that "Oh! It's so close yet so far!" moments. This alleviates my frustration and hoping to keep my sanity together (perhaps, I'm overexaggerating on this). Until then, hoping Brilliant.org will allow users who got the wrong answer still post their solutions on the comments section of the problems. Until then... John, signing off! :"D
PS: Please feel free to give a critical feedback regarding my explanation in the comments section below. Whether it be correcting some lacking to my solution/explanation, elaborating more the concepts behind the problem that I solved, or any other else, it will be really beneficial to learn from you guys. I'm willing to hear it from you so I can further improve my explanation skills. Thank you. :"D
PS 2: I thank @Jason Gomez for checking out my mistake on the previous solution. Your valuable response make me understand more about the derivation of formulas like this. If you are curious to the discussions we made in the comments section below, I will post a history note attachment to make all of you, readers, have a sense on what is going on. I highly suggest you read our discussions.
Historical Note 2021.1.1: Previous faulty solution:
You can click on the image to zoom in better. Thanks. ;)