Dynamics question -- 3 masses on a pulley-rope system on an inclined plane

In summary, the conversation involves a provided image and the completion of the first part of a question, resulting in calculated values of a = 4.8m/s^2, T1 = 24.5N, and T2 = 34.3N. The individual is uncertain about the accuracy of their answers and asks for clarification on solving for mass in static equilibrium. Another individual suggests posting their work for further assistance. A different method is attempted, resulting in a slightly smaller value of a = 4.1, but it is pointed out that the effects of mass accelerations and friction on tensions were omitted. The importance of typing equations is also emphasized, and there is discussion about the calculation of T1 and the acceleration of
  • #1
rabsta00
3
0
Homework Statement
A mass m is 5kg and another mass, M=6kg. Find the acceleration of this system if the kinetic friction is 0.1 and theta = 30 degrees. Find all tensions of connecting ropes. For which values of M will the system stay in an equilibrium position?Assume that the static friction coefficient is 0.15. Disregard the mass of the pulley and ropes.
Relevant Equations
F=ma
Screen Shot 2021-03-29 at 12.31.31 pm.png

This image was provided, I've completed the first part of the question and got a = 4.8m/s^2 as well as T1= 24.5N and T2=34.3N. not sure about my answers though. also I don't understand the mass in static equilibrium part, can anyone explain how to solve that? Thanks.
 
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  • #2
rabsta00 said:
got a = 4.8m/s^2
I get a far smaller value. Please post your working.
 
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  • #3
haruspex said:
I get a far smaller value. Please post your working.

IMG_2060.jpg

I tried a different method but ended up getting a = 4.1 which isn't much smaller.
 
  • #4
You omitted the effect of the mass accelerations and friction on the tensions.
 
  • #5
rabsta00 said:
View attachment 280501
I tried a different method but ended up getting a = 4.1 which isn't much smaller.
Please take the trouble to type equations in. It makes it much easier to quote lines to comment on.
You have T1=2mg sin(θ)-mg sin(θ). How do you arrive at that?
Your calculation of the acceleration of 2m ignores the string. You just have it sliding down the slope unrestrained.
 

1. How do you calculate the acceleration of the masses in this system?

The acceleration of the masses can be calculated using Newton's second law of motion, which states that the net force acting on an object is equal to its mass multiplied by its acceleration. In this system, the net force is determined by the difference between the tension in the rope and the weight of the masses. The acceleration can be found by dividing this net force by the total mass of the system.

2. What is the relationship between the angle of the inclined plane and the acceleration of the masses?

The angle of the inclined plane affects the acceleration of the masses in two ways. First, it determines the component of the weight of the masses that acts parallel to the plane, which contributes to the net force. Second, it affects the normal force exerted by the plane, which can counteract the weight of the masses and reduce the net force. As the angle increases, the component of the weight parallel to the plane increases, leading to a greater acceleration. However, the normal force also increases, which can reduce the net force and ultimately decrease the acceleration.

3. How does the mass of the pulley affect the system's dynamics?

The mass of the pulley does not directly affect the acceleration of the masses in this system, as it does not contribute to the net force. However, the mass of the pulley can affect the tension in the rope, which in turn affects the net force and the acceleration. A heavier pulley may have a greater inertia, which can cause a delay in the tension response and lead to oscillations in the system.

4. Can you determine the individual accelerations of each mass in the system?

Yes, it is possible to determine the individual accelerations of each mass in the system by using the equations of motion and considering the forces acting on each mass. However, in this system, the masses are connected by a single rope and move together as a unit, so their individual accelerations may not be as relevant as the overall acceleration of the system.

5. How does the friction force on the inclined plane affect the dynamics of the system?

The friction force on the inclined plane can have a significant impact on the dynamics of the system. It acts in the opposite direction of the motion and can reduce the net force, leading to a lower acceleration. Additionally, the coefficient of friction can vary depending on the surface and the masses involved, which can further affect the dynamics of the system. In some cases, the friction force may be great enough to prevent the masses from moving at all.

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