Thread: Problem

A boy travelling in a railway carriage decides to try to calculate the acceleration of the train. he suspends a parcel of mass 2kg from the roof of the carriage with a string and measures the angle that the string makes with the vertical, when the train is travelling with a constant acceleration of a ms^(-2) the angle is 8 degrees. find the value a


thanks for any help

Hey! No one has answered yet, so I might as well give it a shot! (it's been a while). I'm not sure what you mean by ms^(-2) though. But in any case:

I used:
F= mg
F=2kg(9.8m/s^2)
F=19.6N (the gravity that would pull the object down). But it's on an angle, so you have to imagine a right angled triangle. 19.6 is the value of the vertical part of the triangle. We know the top angle in the triangle is 8. Using tan to get the horizontal force (the force pulling the weight out by 8 degrees) :
tan8 = x/19.6 x = 2.75N (This is caused by the trains movement).
So then:
F=ma
2.75N = (2kg)(a)
a = 1.375m/s^2

I hope it's right... anyone else have other solutions?