“Take a simple idea and take it seriously”
- Charlie Munger, Vice-Chairman of Berkshire Hathaway
This quote taken from Charlie Munger, best describes the invention of the retractable pen. The mechanism behind the retraction and the extension of a pen may appear straightforward but the impact it has made in people’s lives is larger. As a student, I have to use a pen in my everyday work and without it I cannot get any of my assignments done. In the process of using it, I always wonder how a simple spring within a pen, plays a major role in the functioning of the pen. This led to my interest in finding out that the concept of Hooke’s Law is responsible for this. The force created when the end of a pen is pushed leads to the extension of the spring
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In my IA, I will be investigating the effect of different masses on a spring in order to determine its spring constant. I will also be comparing between the 2 different methods that I will be using to determine the spring constant. I have used a static method by measuring the displacement of the spring and a dynamic method by measuring the time taken for 15 oscillations by the spring due to different masses.
Hooke’s Law Hooke’s Law states that the stress applied to an object is directly proportional to the strain produced, when within the elasticity limit. The helical spring works based on this
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This shows that which is inline with the definition of simple harmonic motion.
, where is a constant.
refers to angular frequency that is defined as and equates to .
The periodic time for simple harmonic motion is . Therefore the period of a mass-spring system is given by . In order to obtain a linear graph and determine the spring constant from the gradient, the equation is squared. Hence,
The value in the above equation needs to take into account the mass of the spring as well. This mass would be taken be the effective load of the spring. However, this value does not consider the whole spring mass but instead a smaller part of it. This is because the entire spring does not vibrate with the same amplitude as the load. Hence, .
From this equation, the graph of against would be plotted. The gradient, , will be used to determine the spring constant and the y-intercept, to determine the .
Experimental Design
Determining Displacement of
Before the gymnast jumps on the springboard the board and springs have potential energy. When the gymnast jumps on the springboard it turns into kinetic energy and causes the board to push the gymnast up. The larger number of springs in the air board have more potential energy which leads to the hypothesis that it will provide the greatest
To begin the experiment, we measured the masses of the two stoppers and the eye bolt used to secure the stoppers that we were using in our apparatus. The mass of the first stopper was 18.8 grams and the mass of the second stopper was 50.5 grams. The mass of the eye bolt was 11.6 grams. The mass of the screw and bolt that secured our hanging mass was given to us as 25 grams. After, we chose six different hanging masses based on stopper mass. We made sure that the hanging mass was always larger than the stopper mass or else we would not be able to get the stopper to spin at a constant velocity. The first three mass ratios we chose was using the stopper with the mass of 18.8 grams and then we used a hanging mass (the mass of the screw and bolt is included) of 65 grams, 85 grams, and 105 grams. This gave the three mass
After collecting data and analyzing the results the group concluded that tension will always be greater than mass for uniform constant motion due to the presence of θ. As the length of the string for the flying toy increased, θ decreased in both trials for the cow and bat. For instance, when the bat had a length of 0.86m, the calculated θ was 34.4°, but when the length was shortened to 0.61m, the θ increased to 36.5°. The period was also shortened when the length decreased; therefore, velocity decreased as string length increased while acceleration increased with a
First, we will set up the force table. The table comes in three separate pieces the base, stand and table once we connect and fasten all three parts we must use a circular level to make sure the table is balanced. If the force table isn’t balanced then we must adjust the base’s feet to the appropriate levels on each leg till the bubble on the level is centered. We must then assign where the positive & negative x, y axis are on the force table as a point of reference and label them with tape .Then for part I we must apply 1.96 N in the positive x – direction, and 2.94 N in the positive y-direction then we must balance the two with a third force and record the magnitude and direction of it and a draw a diagram showing all three forces. Part II
handset can give force to a spring loaded operating arm, which is connected to a
How well did your calculations of the string’s mass per length compare? Of the changing mass and changing frequency methods, which do you feel gave the best results and why?
10. How does varying the frequency effect contraction force? Which interval caused the greatest contraction?
This forms the function y=3.455. The solids of revolutions would look like the following images.
At age 20 Robert Hooke becomes a scientist, he had the abilities to do mechanical instruments.He became very famous for inventions he made. The inventions that he made that we know today are the Universal Joint,Telescope,Balance Wheel,and the Diagram.Because of his inventions people called him Hooke England’s Leonardo Da Vinci.He impressed his teacher by learning Greek and latin,and learning six old books in mathematics called “Euclid’s Elements’’ less than a week.He was described as polymath because he excelled various disciplines of astronomy and biology,to architecture,paleontology and even medicine.
Exercise 2: Skeletal Muscle Physiology: Activity 3: The Effect of Stimulus Frequency on Skeletal Muscle Contraction Lab Report Pre-lab Quiz Results You scored 100% by answering 4 out of 4 questions correctly. 1. During a single twitch of a skeletal muscle You correctly answered: b. maximal force is never achieved. 2. When a skeletal muscle is repetitively stimulated, twitches can overlap each other and result in a stronger muscle contraction than a stand-alone twitch. This phenomenon is known as You correctly answered: c. wave summation. 3. Wave summation is achieved by You correctly answered: a. increasing the stimulus frequency (the rate of stimulus delivery to the muscle). 4. Wave summation increases the force produced in the muscle.
Then, notes were taken of the mass and the force of the weight, and continue with varying weights. Once all the data was collected, the program LoggerPro was used to create a data table. Once the table created in LoggerPro, a scatterplot that shows the relationship between mass and force was created. Then, the best fit line for the data was found, and also the mathematical model. Lastly, the relationship between these two variables were
The line of best-fit is used to find the gradient, the T2/L value, if straight or linear it shows that the relationship between the two is directly proportional. Using the original equation, you can square both sides and rearrange it to make . Then you can input the gradient value (T2/L) and work out g. , where g equals 10.13 m/s2. This value is close to the
The forces that are involve with the experiments are basically focused on the concurrent forces. The experiment also allows us to develop the condition of balancing or arranging the angles both sides on a force table. This laboratory experiment allows us to take the mathematical abstraction of a vector to make it tangible as possible. This experiment will look into two ways of
Purpose: The purpose of the practical is to find how mass affects acceleration and how it affects also the force of the accelerating body. To do this we are going to do the ticker tape experiment where an accelerating body pulls a tape through a consistent 50 dot per second ticker timer. The acceleration body in this experiment will be a small trolley pulled by a string that is pulled by the downfall of different masses which will then tell how mass affects acceleration.
Since the base length is also the time taken it follows that the area under the graph is the