The outcome variable that I am going to measure in this investigation will be the deflection of the ruler in mm, I will do this by looking at the reading horizontal to it so that the reading are not affected by the angle of which I read them from.
The equipment I will need for my experiment will be;
- Two meter rulers
- One G-clamp
- One set of weights measured in intervals of 1 N (100 grams)
- String
These are the methods I will use to obtain my results.
1. I will clamp the ruler to a secure hangover E.g.: a table edge, using the G-clamp.
2. Next, I will place a ruler vertically next to the ruler acting as a cantilever so that I can read the measurements clearly against it.
3. Then, I will record the deflection of the ruler acting as a cantilever against the vertical ruler.
4. I will add a force of 1 N (100 grams) to the end of the cantilever, by hanging on the string tied to the end of the ruler, and record the deflection of the ruler acting as a cantilever
5. I will then continue to repeat step 4 adding a force of 1 N each time until I reach a total of 7 N.
This is a diagram of how I will set up my apparatus.
To make my investigation safe, I will take care whilst handling the weights not too drop them and cause injury, I will make sure that I only use a maximum amount of weights which will not snap the ruler. I will do the investigation in a safe place where people are not trying to move around.
To make my investigation accurate, I will measure my results in mm, check that all the 1 N weights are accurate by weighing them, and use an accurate way of measuring the deflection.
To make my results reliable, I will repeat the investigation three times and take an average of them. When I have drawn my graphs, I will justify and explain them.
Prediction – I predict that when the force on the ruler is doubled, the deflection of the ruler will double. Hopefully you will be able to see this from my graph; by this I state that the cantilever will obey Hook’s law. I predict that there will be a definite increase with larger turning effect (moment) when more force is added. The amount of deflection will be directly proportionate to the amount of force applied. Also, I believe that doubling the force, will double the deflection, my reasoning for this are that the amount of force applied to the ruler will push it down due to gravitational force which is being applied. This will cause the ruler to bend and stretch due to its elasticity.
In the experiment, when force is applied to the cantilever the top side of the ruler, will become stretched, its molecules wider apart whereas the bottom side of the ruler will be compressed with its molecules closer together.
Earlier work that I have done with springs, shows that when something is under a force which makes that compress or extend they will obey ‘Hook’s law’ which states that deflection is directly related to the force, and that when a force is doubled, the compression or extension or in our case deflection will also be doubled.
Sources of information – I used information from our physics lessons, from our physics textbook “physics for you” and from the Hutchinson encyclopaedia pg. 762.
Results –
Set 1
Set 2
Set 3
Averages
Analysis – From my graph, I can see that the force is directly related to the deflection. I can tell this because the graph is in a straight line.
Also from my graph, I can see that when the force is doubled the deflection is doubled. I can see this because when I drew a straight line from 2 N up to the line of best fit, it read 50 mm deflection then when I read up from 4 N the deflection was 100 mm. This means that my results agree with hook’s law.
Stiffness constant – K = F (N)/D (mm)
So F = K D
K = 1/22.33 = 0.04 N/mm K = 0.04 at 1N
K = 2/49.67 = 0.04 N/mm K = 0.04 at 2N
K = 3/78.33 = 0.04 N/mm K = 0.04 at 3N
K = 4/99.67 = 0.04 N/mm K = 0.04 at 4N
K = 5/128.0 = 0.04 N/mm K = 0.04 at 5N
K = 6/149.33 = 0.04 N/mm K = 0.04 at 6N
K = 7/177.00 = 0.04 N/mm K = 0.04 at 7N
This proves that my prediction is right, because the constant stays the same all the way through.
Evaluation –
My procedure was good enough to make my measurements reliable as I got another person to read them as well as me.
I can tell that my results are reliable as my line of best fit is a straight one which passes through the point 0, 0 and all of the points lie close to the line of best fit. I can tell that they are also reliable as they graph agrees with Hook’s law.
I did not have any anomalous results in my investigation as all of my results fit in with my pattern.
From the above, I believe that my results were accurate enough, although if I was to do the investigation again I would take more results at more regular intervals. E.g. Every 0.5 N so that my results were even more accurate because I would be taking more results.
My graph shows me what I needed to see, but if I had more results, I would be able to see a better line. This would allow me to get a better conclusion of my results. From my graph I can see that when the force is doubled so is the deflection.
Overall, I believe that my investigation was conclusive enough for what I wanted to know but could have been more accurate if I wanted it to be. My results show that the deflection is directly related to the Force, and that when the force is doubled the deflection is doubled this agrees with Hook’s law.
Jack Cummins 10LB