Dynamics problem with a fluffy (Mimix)

[Mimix]

A block and a fluffy are connected by a light cord over a frictionless pulley. The 8 kg fluffy sits on a plane inclined at 25 degrees. Determine the magnitude and direction of the acceleration of the system as well as the tension of the cord(coefficient of static friction is 0.21)

I also based this fluffy on gr1m’s artstyle

[xixicoco477]

i should have paid more attention in physics class

[ezpete]

This is dynamics, not physics. I can solve this as its an engineering class I took, i just dont feel like it atm.

[Maple]

I started solving it but I spilled water on my textbook and the fluffy drowned. Can I get an extension on this assignment?

[Mimix]

Of course!!

[grimbusiness]

eleven

[X115-1]

8kg? What a fat fuck. Sounds like it should be turned into a litter pal to thin it out some.

[Grim]

Alrighty, the prompt leaves out a few things that I think can be safely assumed here, but I’ll still write them out, just to be safe.

• The bottom of the triangle/wedge is on a level plane orthogonal to the force of gravity , F_g.
• Any force that the fluffy exerts is either ignored for the purposes of the problem, or small enough that it can be safely ignored.
• The tension on the cord is calculated at the instant the fluffy-cord-weight system starts moving, as this is not specified, but given that the static C_f is given, this seems to be the implied desired answer- @Mimix work on question wording here, regardless of whether I have guessed your intent correctly or not- that I had to guess is not good.
• The acceleration is also calculated at the instant the system starts moving, as this is the only time for which we have a C_f value- again, that I have to guess what moment’s acceleration you desire to be calculated is not good.
• I again have to guess that you mean that the coefficient of static friction is for the fluffy and not the weight. Seriously write more in your question, you wrote so little here it’s like each letter physically hurt you or something.
• Finally, I figure that you are asking for the average acceleration vector across the weight-cord-fluffy system… I think… Either way, that’s what I’ll solve for here today.

Remember kids- If you communicate poorly, someone else ends up having to decide what your words mean for you. (That said, I do LOVE that you made a problem with fluffies in it <3)

OK, now for answers

55 lb is ~24.9476kg, and 25* /90* =0.27 repeating, so that’s the fraction of F_g (9.8m/s^2) we get to use, with the 8kg fluffy this brings us to this:

8kg* 0.2777…* 9.8m/s^2

then since our coefficient of static friction is 0.21, that leaves us with 0.79 of the rest of the at the instant motion starts where we are calculating everything, so we then multiply by 0.79 to get:

8kg* 0.2777…* (9.8m/s^2)* 0.79=17.2044444… (kg* m)/(s^2)= 17.20444444… Newtons

this is the force of the tension on the cord, by the way.

using F=ma we show that the weight will accelerate at ~ 0.6896m/s^2, which must also be the acceleration of the fluffy to which it is tied and from which it is receiving the force that is accelerating it.

so the weight accelerates along +x, and the fluffy accelerates along the plane which is 25 degrees below +x. Given their relative masses, that leaves us with an average acceleration angle of 5.99 degrees below +x, at ~ 0.67344m/s^s

here’s some work

[Mimix]

(post deleted by author)

[Mimix]

Yeah this problem was from a timed quiz that I got frustrated. I rewrote it from memory so that’s why its a bit iffy. I’ve been waiting for my professor to reveal the answers so I’ll let you know if you got it right

[Grim]

Mind you, i’m a chemist, and graduated university nearly a decade ago, so maybe thirteen years since i’ve had anything like this, but with that said, did you end up going about it roughly the same way?

I love that we have one @gr1m_1 to do epic art and comics and another @Grim to science and writing.

[BrotherOni]

Whoa. I’m gonna need a cold shower after all that filthy calculation work.

[Grim]

Filthy as in this just caused math/physics flashbacks, or filthy as in you’re pretty sure that I can almost certainly write/sign prescriptions and a pharmacist would fill them without a second thought, based on my handwriting?

[BrotherOni]

Yes.

[Pushka]

My brain started melting halfway through that. I hate math…

[Grim]

Did you ever get the answer to this back from your prof?

[Mimix]

He still hasn’t revealed it yet, I’m thinking of just going to his office hours tomorrow

[Grim]

for kicks, can you bring him my answer too?

[Mimix]

You got it!!

[Grim]

so what happened with this?