(and your arithmetic in your "long approach" was wrong, so it's difficult to check the rest)
Where did I go wrong so I can correct this... Like are my sum of force equations right?
Did I substitute them into other equations wrong? Or is the fact that I didn't use the Y forces at all...
oh well thanks! haha the last 48hr's of physics frustration can do that to a person
ok attempt 2 at shortcut:
pseudo mass: mr^2 / r^2 = 5
M = 5+5 = 10
a= (8(9.81) sin30/10
a= 3.92
Ok let's focus on the long way as its what the question asks I don't think I did that...
gneil does this work for problems with inclines as well?? I have posted a question with an incline, if this trick works for that too that is very handy!
An 8kg mass is initally at rest on a 30 degree frictionless incline, it is attached to a hoop shaped 5kg pulley of radius 25.0cm by a massless cord. Find the tension in the cord and the acceleration of the mass using Newton's Laws.
Ok let's try this again:
∑τ=Iα = Tr
∑Fy=-m2a = T-m2g
I= 1/2mr²Therefore 1/2m1r²(a/r)= m2(g-a) (r)
1/2m1 a = m2(9.81-a)
1/2 (8) (a) = 5(9.81-a)
a= 5.45m/s²
T= (5(9.81-5.45))
T= 21.8N
?I hope your not in my class CHOD! lol
2/5m1r²(a/r) = (m2(g-a) - m1a) (.5)
Okay I took my sum of Torque equation and substituted equations 1 and 2 so that I only have one unknown variable :a
I did this like so:
∑τ= Iα = Fr sin 90
Iα= (2/5m1r²)(α) which alpha is = to (a/r) and set this equal to F r so I have: (2/5m1r²)(a/r) = Fr...