# Solving a Tricky Tension Problem on a Moving Train

• stateofdogma
In summary, a child on a moving train notices that a ball attached to a string hanging from the ceiling makes an angle of 19 degrees with the vertical when the train slows down. The mass of the ball is 175g. The questions are: a) which way will the string tilt and what is the acceleration of the train? b) What is the tension in the string? Using the equations F=ma and the y-direction force balance, the solution is found to be an acceleration of 3.38m/s^2 for the train and a tension of 1.82 N in the string. The FBD diagram in the textbook and the understanding of the acceleration in the y direction are important in solving this problem.
stateofdogma

## Homework Statement

A bored but observant child on a moving train ties a ball to one end of a string and ties the other end to a light fixture on the ceiling of the train. When the train slows down, the child notices that the string is no longer hanging straight down but instead makes an angle of 19 degrees with the vertical. The mass of the ball 175g.

a) will the string tilt forward or backward? Find the acceleration of the train.

b) What is the tension in the string?

## Homework Equations

$$F=ma$$

## The Attempt at a Solution

Sadly although this question had a complete solution i did not understand it.
First the drawing in the textbook made no sense.(I've provided I file below)
This is my FBD( second in attachments)

these are my equations

$$F_y = -T\sin\theta - mg = ma_y$$
$$F_x= -T\cos\theta = -ma_x$$

I didn't get far in trying to reduce, the solution in the book is acceleration 3.38m per second squared and the tension is 1.82 N.

#### Attachments

• FBD example 5-17.jpg
4.8 KB · Views: 360
• My FBD example 5-17.jpg
5.3 KB · Views: 366
Your force balance in the y-direction is incorrect. The T term and the mg term should have opposite signs. Also, what is your understanding of what the acceleration in the y direction is? Also, your FBD diagram shows that the angle of the string with the horizontal is 19 degrees, rather than with the vertical. Use the y force balance to solve for the tension T.

Chet

I see my mistake on the y axis( that was a typo) but are you saying that the Fy is equal to mg by Newtons third law and then that Fx is equal to the (acceleration of the train) and the mass of the ball. And thanks that's quite illuminating

## What is a tricky tension problem on a moving train?

A tricky tension problem on a moving train refers to a situation where forces acting on an object on the train, such as ropes or cables, create a complex and difficult to solve tension system.

## Why is solving a tricky tension problem on a moving train important?

Solving a tricky tension problem on a moving train is important because it ensures the safety and stability of the train. If the tension problem is not solved, it can lead to derailment or other accidents.

## What are the key factors to consider when solving a tricky tension problem on a moving train?

The key factors to consider when solving a tricky tension problem on a moving train include the weight and position of the object, the speed and direction of the train, and the strength and angles of the tension forces.

## What are some techniques that can be used to solve a tricky tension problem on a moving train?

Some techniques that can be used to solve a tricky tension problem on a moving train include the use of vector analysis, calculating the net force in each direction, and using equations of motion to determine the acceleration of the object on the train.

## What are some safety precautions that should be taken when solving a tricky tension problem on a moving train?

Some safety precautions that should be taken when solving a tricky tension problem on a moving train include wearing appropriate safety gear, having a clear understanding of the train's speed and direction, and working with a team to ensure proper communication and coordination.

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