# Blocks and Strings, Force Analysis

• phoenixXL
In summary, the conversation discusses the problem of finding the acceleration of a block connected to a particle by a string, assuming smooth contacts. The equations used include F=ma, normal and string constraints, and translational equations. After some attempts, the correct answer is found to be 4mg/(17m+M).
phoenixXL

## Homework Statement

A block of mass M is connected with a particle of mass m by a light in-extensible string as shown in the figure. Assuming all the contacts as smooth, find the acceleration of the block after releasing the system.

## Homework Equations

F = Mass * Acceleration
Normal Constraint : The acceleration of two particles in contact is same along the line perpendicular to their line of contact.
String Constraint : The length of the string is constant and could be used to find out the acceleration of the corresponding components using differentiation(using geometry).

## The Attempt at a Solution

Using the FBD and Translational equations

The particle will have the acceleration both in x and y direction. The block will have the acceleration in x direction due to tension in the string and contact force .

for block M
$$\ T\ -\ N\ =\ Ma_x$$

The particle's acceleration in the x direction will be the same as that of the block in the x direction in accordance to the normal constraint.

for particle m
$$mg\ -\ T\ =\ ma_y\\ \ N\ =\ ma_x\\ \implies\ T\ =\ (m+M)a_x$$

Using string constraint we get than the particle's acceleration in the y-direction would be 4times the acceleration of the particle in x-direction
$$4a_x\ =\ a_y\\ \implies\ mg\ -\ T\ =\ 4ma_x\\ \implies\ mg\ -\ (m+M)a_x\ =\ 4ma_x\\ \implies\ a_x\ =\ \frac{mg}{5m+M}$$

But the answer I get is wrong and the correct answer is $\frac{4mg}{17m+M}$

phoenixXL said:
$$\ T\ -\ N\ =\ Ma_x$$
Look at all those horizontal sections under tension. What are they pulling on?

1 person
Right that won't be T but 4T.
ie $$4T\ -\ N\ =\ Ma_x$$

, but I am not sure what you are asking for. Can you provide more context or information about the problem? I am happy to help, but I need more information in order to understand the issue you are having.

## What is a block?

A block is a solid piece of material with a rectangular or square shape. It is often used in physics experiments to represent an object with mass.

## What is a string?

A string is a thin and flexible object that can be used to connect or suspend objects. In force analysis, strings are often used to apply tension or support the movement of blocks.

## What is force analysis?

Force analysis is a method used in physics to study the effects of forces on objects. It involves identifying and quantifying the forces acting on an object, and using mathematical equations to analyze their effects on the object's motion.

## How is force analysis used in studying blocks and strings?

In the context of blocks and strings, force analysis is used to determine the forces acting on the blocks and strings, and how they affect the motion of the objects. This can help in understanding concepts such as tension, friction, and equilibrium.

## What are some real-life examples of blocks and strings with force analysis?

Some examples include a pulley system, where a string is used to lift a block by applying tension; a pendulum, where a string is used to suspend a block and study its motion under the influence of gravity; and a block sliding down an inclined plane, where force analysis can be used to calculate the forces acting on the block and predict its motion.

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