# Tension 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 text book 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
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• My FBD example 5-17.jpg
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