A really good problem(Not for everyone)

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In summary, a prism of mass M is placed on a horizontal surface at an angle of alpha. A small block of mass m is attached to the prism via a rope and a pulley, with all surfaces being frictionless. The block's acceleration is equal to the prism's acceleration towards the wall, and the resultant acceleration of the block with respect to the ground can be found using the triangle law of addition. Tension and normal forces must also be considered in the calculations.
  • #1
FedEx
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A really good problem

Hi
A prism of mass M is kept on a horizontal surface having the inclination of alpha. A small block of mass m is kept on the prism. This block is attached to a vertical wall with a massless rope passing over a pulley which is at the free vertex of the prism.Find the acc of the prism wrt to the block m and wrt the ground.
I hope that you people are able to understand the question.As i am not able to upload the figure.

All the surfaces are friction less. Now what i have been trying is that that the acc with which the block m comes down is equal to the acc with which the prism moves towards the wall because the string is unelastic. But here the acc of the prism is wrt to ground and the acc of the block is wrt to the prism so by triangle law of addition the resultant of these two vectors would be acc of block wrt to the ground. So here we can get the value of the acc of the block wrt ground in terms of the acc of either the prism wrt to ground or the acc of the block wrt prism ,as both are same.

Now there is some tension in the string and this tension opposes the motion of the block on the prism but the block tends to move due to mgsin(alpha). But this tension helps the prism to move towards the wall.Moreover we will have to consider the normal force exerted by the block on prism which will also help the prism to move.But i think we will have to again take a comp of N.Also we will have to consider the normal force exerted by the prism on the block.
I think i have included all the forces,are any forces left to include? If no then i think that the equations which i have formed are correct.I would try to post the equations if i my above logic is approved by you people.
 
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  • #2
Now i think that the calculation part needs to be done and the resultant acc of block wrt to the ground should be found out. Please suggest the changes if any in my logic and help me with the calculation.
 
  • #3


I would like to commend you for your thorough analysis and consideration of all the forces involved in this problem. It is clear that you have a strong understanding of physics principles and are able to apply them effectively to solve complex problems.

One suggestion I would make is to draw a free body diagram for the prism and the block to help visualize the forces acting on them. This can make it easier to identify any additional forces that may need to be considered.

Additionally, it may be helpful to consider the equations of motion for both the prism and the block separately, and then combine them to solve for the unknown acceleration. This can help simplify the problem and make it easier to solve.

Overall, I believe you are on the right track and with careful consideration of all the forces and equations involved, you will be able to find the solution to this problem. Keep up the good work!
 

1. What makes a problem "really good"?

A "really good" problem is one that is challenging, thought-provoking, and has the potential to make a significant impact in its respective field. It should also be well-defined and have clear objectives.

2. Why is it important to have a good problem in scientific research?

Having a good problem is essential in scientific research because it provides direction and purpose to the study. It also helps to identify gaps in current knowledge and can lead to new discoveries and advancements in the field.

3. How do you identify a good problem to research?

Identifying a good problem involves considering the current state of the field, potential impact and significance, feasibility, and personal interest and expertise. It may also involve consulting with colleagues and experts in the field.

4. Can a good problem be solved by one person?

In most cases, a good problem will require a team of researchers with diverse skills and expertise to solve. However, there are instances where a single researcher may be able to solve a good problem, particularly if it is well-defined and within their area of expertise.

5. How do you measure the success of a research problem?

The success of a research problem can be measured by the impact it has in the field, such as publications, citations, and practical applications. It can also be evaluated based on the objectives and outcomes set at the beginning of the study.

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