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

In summary, the problem is that the author has not provided a clear definition for each of the variables, and has chosen different co-ordinate systems for the two masses. The author is looking for an equation relating an acceleration of one to an acceleration of the other, but is unable to find one due to this error.
  • #1
infinitylord
34
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
 

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  • #3
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.)
 

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

1. How do you calculate the acceleration of two masses on a pulley on a slanted plane?

The acceleration of two masses on a pulley on a slanted plane can be calculated using the formula a = (m1 - m2)g sinθ / (m1 + m2), where m1 and m2 are the masses of the objects, g is the acceleration due to gravity, and θ is the angle of the slanted plane.

2. What is the relationship between the masses and acceleration in this system?

The acceleration of the system is directly proportional to the difference between the masses and the angle of the slanted plane, and inversely proportional to the sum of the masses. This means that as the masses become more different or the angle of the plane becomes steeper, the acceleration will increase. Similarly, as the masses become more similar or the angle becomes less steep, the acceleration will decrease.

3. How does the angle of the slanted plane affect the acceleration?

The angle of the slanted plane has a direct effect on the acceleration. As the angle increases, the acceleration will also increase. This is because a steeper angle means a greater component of the force of gravity is acting in the direction of motion, resulting in a greater acceleration.

4. Can the masses have different accelerations in this system?

No, in this system, the two masses will have the same acceleration. This is because they are connected by a pulley, which ensures that they move with the same speed and acceleration. The only factor that affects their acceleration is their difference in mass.

5. How does the presence of friction affect the acceleration in this system?

Friction can decrease the acceleration in this system. This is because friction acts in the opposite direction of motion, creating a force that opposes the motion of the objects. As a result, the net force acting on the system is reduced, resulting in a lower acceleration compared to a frictionless system.

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