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Mechanics 2 Coursework - Ladders

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Introduction

Mechanics 2 Coursework - Ladders Chapter 1: Aim and Assumptions The aim of this project is to find out whether theory used in the classroom can be applied to a real life situation with satisfactory predictions, and to test the validity of certain equations in a real life situation. Consider this: A man wishes to climb up a ladder of height l and wishes to know if it is safe. He would use the ladder situation we are able to solve in Mechanics 2, and, assuming there is no friction at the wall, he would be able to calculate the height up the ladder x that the ladder would give way. We wish to test whether this is possible. To do this we use a ruler of length 100cm and rest it against a smooth surface (in this case a whiteboard, which is firmly attached to the wall). ...read more.

Middle

This is less important than my other assumptions, because a small inaccuracy will not make difference to our value. We can see the way in which the model works below: First we place the ruler against a smooth wall (the white board) and then let it slide down in a straight line (so that all the forces involved are in the same plane, ensuring a 2d situation). We take 5 readings of each of these heights along the wall, and from these a value of ? can be calculated, enabling us to work out F and therefore �. If we assume equilibrium, the ladder's weight w combined with the weight of the person will balance with R (if we resolve forces vertically). By taking moments about the base, we find that S x sin? = (w+mg)cos?. We work out w by weighing the ruler, which turns out to be 72.2g. ...read more.

Conclusion

We can firstly predict R for all cases, because it does not have an x in its equation. By N2L, R=0.0722 + 9.81x0.2 = 2.03 The values of x I will measure are not uniform, because this shows that x does not have to be uniform to conform to the predictions made. I used values of 90cm, 75cm, 60cm, 40cm and 20cm. To predict the value of ? at which the ruler will slip, I can put these values for x into the previous equations: x=0.2, R= 2.03 Moments about base, 1*Ssin? = (0.0722*0.5+9.81*0.2*0.2)cos? S = F = �R = 0.4*2.03 = 0.812 sin?/cos? = (0.0722*0.5+9.81*0.2*0.2)/1*0.812 = 0.528 tan?=1/0.528 ?=62.17 The value for z from this value of ? comes to 0.884. The others are as follows: x ? z 0.2 62.17 0.884 0.4 44.68 0.703 0.6 33.79 0.556 0.75 28.30 0.474 0.9 24.26 ?? ?? ?? ?? Alex Hayton Mechanics 2 Coursework - Page 1 of 1 Ladders ...read more.

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