Boxes hanging attached to box on shelf

  • Thread starter whartmann
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In summary, the problem involves a box of mass 3.5kg resting on a frictionless shelf and attached to two hanging boxes with masses 1.5kg and 2.5kg. The system is initially at rest and the goal is to find the tension in each string and the acceleration of each box after it is released. The relevant equations are Ft = m2a and a = m1g / (m1+m2). To solve the problem, analyze the forces on each mass and apply Newton's 2nd law.
  • #1
whartmann
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Homework Statement


A box of mass m2 = 3.5kg rests on a frictionless horizontal shelf and is attached by strings to boxes of masses m1 = 1.5 kg and m3 = 2.5kg, which hang freely as shown in the figure. The system is initially at rest. After it is released, find A) the tension in each string and B) the acceleration of each box

Homework Equations


Ft = m2a
a = m1g / (m1+m2)

The Attempt at a Solution



Not very sure how to proceed, never done a problem with masses hanging on both sides
 
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  • #2
Presumably the strings pass over pulleys? (Diagrams are always helpful.)

Analyze the forces on each mass and apply Newton's 2nd law.
 
  • #3
of a box before.

I would first identify the key variables and forces involved in the problem. In this case, the key variables are the masses of the boxes (m1, m2, and m3) and the key forces are the tension in each string (T1 and T2) and the weight of each box (m1g, m2g, and m3g).

To solve for the tension in each string, I would use the equation Ft = m2a, where Ft is the total force acting on the box of mass m2, and a is the acceleration of the system. Since the system is at rest before it is released, the acceleration is 0, meaning that the total force acting on the box is also 0. Therefore, the tension in each string must be equal to the weight of the hanging boxes, which can be calculated using the equation F = mg.

To solve for the acceleration of each box, I would use the equation a = m1g / (m1+m2). This equation takes into account the masses of both the hanging boxes and the box on the shelf, and the acceleration is dependent on the ratio of these masses.

In summary, to find the tension in each string, I would use the equation Ft = m2a, and to find the acceleration of each box, I would use the equation a = m1g / (m1+m2). However, it is important to note that this is a simplified solution and does not take into account any external forces or friction that may affect the system. Further analysis may be needed to fully understand the dynamics of the system.
 

1. What is the purpose of having boxes hanging attached to a box on a shelf?

The purpose of having boxes hanging attached to a box on a shelf is to maximize storage space and organization. By having the boxes attached to the shelf, it allows for more vertical storage and prevents the boxes from shifting or falling off the shelf.

2. How are the boxes attached to the shelf?

The boxes are usually attached to the shelf with hooks or clips that can be easily secured to the shelf. Some shelves may also have built-in attachments specifically designed for hanging boxes.

3. What types of items can be stored in boxes hanging attached to a box on a shelf?

Boxes hanging attached to a box on a shelf can be used to store a variety of items such as small tools, craft supplies, office supplies, or even food items. The boxes can also be used for sorting and organizing items within a larger storage space.

4. Are there any disadvantages to using boxes hanging attached to a box on a shelf?

One potential disadvantage is that the hanging boxes may limit the overall weight capacity of the shelf. Additionally, if the boxes are not securely attached, they may become unbalanced and fall off the shelf. It is important to properly secure the boxes and evenly distribute weight to avoid any potential issues.

5. Can boxes hanging attached to a box on a shelf be used for long-term storage?

Yes, boxes hanging attached to a box on a shelf can be used for long-term storage. However, it is important to regularly check the boxes and their attachments to ensure they are still secure and stable. It is also recommended to use sturdy, durable boxes for long-term storage to prevent wear and tear over time.

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