Brain Not Braining : Part 6 \ stacker news ~science

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Guess we're all fine so let's get down to business shall we?

Problem:

A box of mass m is placed on a frictionless incline at an angle

\theta

to the horizontal. The box is connected by a light, inextensible rope over a frictionless pulley at the top of the incline to a hanging mass M.

Question: What is the acceleration of the box just after release?

(i know the image looks weird, but it's AI generated and I hope you get the idea)

1,000 sats bounty

noknees's bounties

The masses and the pulley are irrelevant when you ask about the acceleration?

sin(\theta) \times 9.81 \frac{m}{s^2}

no but the pulley is a frictionless bearing but with moment of inertia I and radius R (to be included for rotational effects)

Haha that image itself is like a MC Escher painting

lol true

F net M = M * a = Tension - M * g

F net m = m * a = m * g * sin(ɵ) - Tension

adding the two equations: a(M+m) = g [m * sin(ɵ)] - g * M

final answer: a = g {[m * sin(ɵ)] - M}/(M+m)

good review in 11 min here;