How to find acceleration of 2 masses on a pulley on slanted plane

AI Thread Summary
To find the acceleration of two masses on a pulley on a slanted plane, it's essential to establish a consistent coordinate system for both masses, as the string length constraint relates their accelerations. The equations of motion for each mass need to be correctly defined, particularly ensuring that the acceleration for m1 is not mistakenly set to zero. The normal force and friction must also be accurately calculated, as errors in these values can lead to incorrect results. A clear definition of all variables is crucial to avoid confusion and errors in calculations. Addressing these points will help in solving for the acceleration effectively.
infinitylord
Messages
34
Reaction score
1
---see attachment for picture of problem---
There is no actual numbers given. We are supposed to be solving for acceleration and I tried but can't find an answer. I'll show you my work and please tell me what I did wrong

Ʃfx= Ff + T - w1sinθ = m1ax = 0
Ʃfy= N - wcosθ = m1ay
Ʃfx= 0 = m2ax = 0
Ʃfy = T - w2 = m2ay
Ff = μN --- w2 = m2g

then I began to plus stuff in
T = m2g + m2ay or T = m2(g + ay)
μN + m2g + m2ay - w1sinθ = 0

then I tried to solve for normal force and got
N = (w1sinθ - m2g +m2ay)/μ

I then tried to plug N into [N - w1cosθ = -m1ay]
(w1sinθ - m2g +m2ay)/μ - w1cosθ = -m1ay

I tried to solve from there for acceleration
w1sinθ - m2g + m2ay = -m1ay + w1cosθ * μ ----
w1sinθ + ay = (-m1ay + w1cosθ + m2gμ)/m2
a = -m1ay + w1cosθ + gμ - w1sinθ

obviously acceleration cancels out my way and that means I can't solve. So any help on how to do this problem would be greatly appreciated
 

Attachments

  • IMAG0151.jpg
    IMAG0151.jpg
    29 KB · Views: 490
Last edited:
Physics news on Phys.org
infinitylord said:
Ʃfx= Ff + T - w1sinθ = m1ax = 0
Ʃfy= N - wcosθ = m1ay
Ʃfx= 0 = m2ax = 0
Ʃfy = T - w2 = m2ay
Ff = μN --- w2 = m2g
It's difficult to pinpoint the error without an actual definition for each of the variables. In fact, failure to lay out such a definition in advance is often the source of the error.
Clearly you have chosen different co-ordinate systems for the two masses, and that's fine. But the constancy of string length gives you an equation relating an acceleration of one to an acceleration of the other. What is that equation?
(You have the wrong acceleration equated to zero for m1. Maybe that's just a typo in the post and is not propagated in later working - I haven't checked.)
 
Thread 'Variable mass system : water sprayed into a moving container'
Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...

Similar threads

Replies
23
Views
3K
Replies
35
Views
4K
Replies
19
Views
4K
Replies
5
Views
2K
Replies
1
Views
2K
Back
Top