# Can someone check my solution to this block and tackle problem

• vande060
In summary: Your Name] In summary, the conversation is about a problem with a snapshot of an online book and the use of equations to find the acceleration and tension of a system with pulleys and masses. The person providing the summary points out a potential mistake in the final equation and suggests labeling the masses and pulleys for clarity. They also offer encouragement and an invitation for further discussion.
vande060

## Homework Statement

you absolutely need to check the link for my problem picture; this is a snapshot of my online book.

http://s861.photobucket.com/albums/ab174/alkaline262/?action=view&current=prob9-1.jpg

f=ma

## The Attempt at a Solution

as you can see from the picture I have let each of the strings dangling be represented by an x value

so:

3x1 + x2 = length of rope

differentiating twice

3a1 + a2 = 0

and the equations for m1 and m2:

m1a1 = -3T + m1g

m2a2 = -T +m2g

next step is to add these two equations together and set equal to zero

3(a1 = -3T/m1 + g)

+(a2 = -T/m2 +g)
----------------------

3a1 + a2 = 4g -T( 9/m1 + 1/m2) = 0

solving for T = 4g/( 9/m1 + 1/m2)

then i can just plug this into the above a1 and a2 equations to get acceleration right??

and the tension of that tiny little rope below the center pulley till be 2T.

what do you think? Have I made any mistakes

?

Thank you for sharing your approach to solving this problem. I appreciate how you have represented the strings with x values and used differentiation to find the accelerations. Your equations for m1 and m2 also seem correct.

However, I would recommend double-checking your final equation for T. It seems like you have made a small mistake with the signs, as the tension should be positive since it is pulling up on the masses. Additionally, it may be helpful to label the masses and pulleys in your equations to keep track of which values correspond to which objects.

Overall, your approach seems reasonable and I think you are on the right track. Keep up the good work! If you have any further questions or would like to discuss your solution further, please don't hesitate to reach out.

## What is a block and tackle problem?

A block and tackle problem is a type of mechanical problem that involves using a system of pulleys and ropes to lift heavy objects.

## How do you solve a block and tackle problem?

To solve a block and tackle problem, you must first determine the weight of the object being lifted and the number of ropes and pulleys in the system. Then, you can use the principle of mechanical advantage to calculate the force needed to lift the object.

## What is the principle of mechanical advantage?

The principle of mechanical advantage states that by using a system of pulleys and ropes, you can reduce the amount of force needed to lift an object. This is achieved by distributing the weight of the object among multiple ropes and pulleys, thereby increasing the mechanical advantage of the system.

## Can someone check my solution to a block and tackle problem?

Yes, you can ask someone to check your solution to a block and tackle problem. It is always helpful to get a second opinion and ensure that your calculations are correct.

## What are some common mistakes when solving a block and tackle problem?

Some common mistakes when solving a block and tackle problem include forgetting to account for the weight of the ropes and pulleys themselves, not properly estimating the friction in the system, and making errors in the calculations for mechanical advantage. It is important to double check your work and make sure all factors are accounted for.

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