Simple problem for anyone who knows what he is doing

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In summary, the conversation involves a problem with a cord that has mass. The formula for the acceleration of the system is given as a=(m2+mc(L2/L))g/(m1+m2+mc). The conversation also discusses the mass of the cord and how to calculate it, as well as the force of tension and its effects on the system. The final step is solving for the acceleration using the equation F=ma.
  • #1
Suicidal
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I’m stuck on a problem involving a cord that has mass. I know how to do problems where the cord's mass is 0 but ones the factor of the cords mass is introduced I’m lost.

I’m stuck on the following problem:

A block (mass m1) on a smooth horizontal surface, connected by a cord that passes over a pulley to a second block (mass m2), which hangs vertically.

Determine a formula for the acceleration of the system if the cord has non-negligible mass mc specify in terms of L1 and L2 the lengths of cord from the respective masses to the pulley (total cord length L =L1+L2)

How do I approach this problem?

The answer (if it helps) is a=(m2+mc(L2/L))g/(m1+m2+mc)

Any help will be highly appreciated.
Thanks
 
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  • #2
I think what you need to do is note that the cord has total length L= L1+ L2 and so has "linear density" mc/L= mc/(L1+ L2). That means the mass of the cord hanging vertically is
mc(L2/(L1+ L2))= mc(L2/L). That gives precisely the answer given.

From that you can calculate the total mass hanging down and total of all mass.
 
  • #3
I already understood that the mass of the cord hanging down in L2/L.

How do you deal with the fact that the horizontal part of the cord is being pulled down and what about the tension in the cord?

I don’t understand how all the forces involved effect the system and therefore I don’t know how to set up an expression for the acceleration.


For the hanging down part of the system Net force = (m2+mc*L2/L)*g- Ft
Where Ft is the force of tension.

So
a=((m2+mc*L2/L)*g- Ft)/( m2+mc*L2/L)

I think I’m correct on that, but how do I find Ft.
 
  • #4
I thought you said you could do it if the cord was massless- once you know how to calculate the mass of each part of the cord, include that into the masses m1 and m2 and the rest of the problem is exactly as if the cord was massless.

The total mass "hanging down" is m2+ mc(L2/L). The downward pull is it's weight: (m2+ mc(L2/L)g. But that force (weight) has to accelerate the entire mass: m1+ m2+ mc. Using F= ma we have

(m2+ mc(L2/L)g= (m1+ m2+ mc)a.

Solve for a.
 
  • #5
Thanks, the explanation helped a lot .
I think I understand now, but there is still one thing, the force of tension.
 
Last edited:

What is a "simple problem" in science?

A simple problem in science is a problem that can be easily understood and solved using basic scientific principles and methods. It usually involves a straightforward experimental design and can be replicated by others.

What does it mean to "know what he is doing" in science?

In science, "knowing what you're doing" refers to having a strong understanding of the scientific method, research techniques, and the subject matter at hand. It also involves being able to critically analyze data and draw accurate conclusions.

Why is it important to have knowledge and skills in science?

Having knowledge and skills in science allows individuals to better understand the world around them and make informed decisions. It also helps in solving problems and developing new technologies and innovations.

What are some examples of simple problems in science?

Examples of simple problems in science include determining the boiling point of water, testing the effects of different fertilizers on plant growth, and measuring the density of various substances.

How can one improve their problem-solving skills in science?

One can improve their problem-solving skills in science by practicing the scientific method, keeping up with current research and developments in their field, and seeking guidance from experienced scientists. Additionally, staying curious and asking questions can also help develop problem-solving skills in science.

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