here's my lab
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sharekey=078256673f2b4a3dd9d5c56d04dfa8b0e04e75f6e8ebb871
copy the link this might help you understand what I'm doing I have completed it I just need help with question 2 which I have already posted
I hope you got microsoft 97-2003
thanks for the help
Starting from your results, you have the maximum energy in the spring.
That maximum energy will be equal to the PE + KE
When at the equilibrium point, that means KE=Energy in 2b
so solve for velocity...
1/2 m v^2 = energy in 2b.
d)Now wnen at 1/2 amplitude, the must be (1/4) max (remember 1/2 kx^2), so the pe is 1/2 kx^2 or 1/4 the max. That means the KE must be 3/4 the max.
Check my thinking.
can you look at my lab and tell me how to do 2
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Yes, I have got the file.
Here is the content, for those who are interested. Will get back to you after finished reading.
Physics in the Spring
Introduction
The concept of this lab that is being investigated is simple harmonic motion. Our textbook provides the following definition, “vibration about an equilibrium position in which a resorting force is proportional to the displacement from equilibrium”. The purpose of this lab is to find several different spring constants and then to solve for the period of the spring. In this experiment I will be using different masses attached to a spring and then recording its displacement and finding the spring constant. I will then set the spring into oscillation and record the period. I will then calculate the period and compare these two values.
Sketch
Materials
· Spring Stand (attached onto it is a ruler that was also used)
· Spring
· Mass stand
· Several different masses
· Stop watch
Procedure
1.) Using at least three different masses, generate a graph of displacement (x- axis) vs. Force (y-axis) for your spring. Use at least three data points.
2.) Using the slope of this graph, determine the spring constant, k, of your spring.
3.) Using the pointer and the scale, note the equilibrium position of your mass on the spring, pull the mass down a given distance, record it, and release the mass. Record the position that the mass rises to. Do this for each mass.
4.) Using three different masses, set the system in oscillation and measure the time required for ten oscillations for each mass. Using this data, determine the period, T, of each mass on the spring.
5.) Compare the actual period, with the predicted period determined from your spring constant determined in step 2.
Data
gravity = 9.81 m/s^2
Equilibrium Position with no Mass= .90 cm ± .5 cm
mass of stand = 17.4 g ± 5.0 g
Mass (g) Equilibrium Position with Mass (cm) Amplitude (cm) Δt (for 10 oscillations) (s)
30 1.8 ± .5 4.0 ± .5 3.3 ± .5
50 2.5 ± .5 4.0 ± .5 4.7 ± .5
100 4.5 ± .5 4.0 ± .5 5.2 ± .5
Observations
I observed that when I performed step three in the procedure that I pulled the mass spring system down 4.0 cm from the equilibrium position with mass that it went past this equilibrium position 4.0 cm. I observed this for every single different mass that was used to conduct this experiment.
Analysis
We know this to be so because when it’s in equilibrium it’s in equal barium and the net force is zero when all of the present forces acting on it are added together and it’s not moving anywhere. The two forces that are present are elastic and gravity. We can derive the next formula with this reasoning.
We can now simplify this equation using the following formulas:
Hooke’s Law
Force of Gravity
We can then rearrange this formula for the spring constant, k.
Using this graph below the spring constant, k, can be found using the formula for slope.
Slope
Plugging our variables in, the force of gravity and displacement, for our graph we get this formula.
Using what we have already established above we can simplify the formula.
This formula gives us a modified formula from the one we already have established to find the spring constant. So we set the slope equal to the spring constant, k.
The work below is a sample of the first mass.
This graph shows the force of gravity with respect to their displacements. This graph shows that as the force of gravity decreases the displacement also decreases along with the slope, the spring constant.
In order to find period observed I need to take my recorded time for ten oscillations and divide it by ten to get the time of one period. The first period will be used as a sample.
In order to calculate the period I’ll use the formula provided in our textbook.
Period of a Mass-Spring System in Simple Harmonic Motion
I’ll calculate the period using the data collected for the first mass and the value I calculated for the spring constant in my analysis, k, as a sample for this calculation.
Below is proof that the units do actually cancel out.
In order to find the percent error between the two times the following formula will be used:
Percent Error
In this lab the experimental value is the period, , sense it was found throughout performing this lab, and the accepted value is the period, , sense it was the actual period that occurred. The percent error for the first mass will be used as a sample for this calculation.
Mass (kg) Fg (N) x (m) k (N/m) T (observed)(s) T (Calculated) (s) Percent error (T observed Vs. T calculated) (%)
0.05 -0.49 -0.01 49 0.33 0.20 40
0.07 -0.69 -0.02 35 0.47 0.28 40
0.117 -1.15 -0.04 29 0.52 0.40 23
Conclusion
The purpose of this lab was to find several spring constants, observe the periods of a spring, and calculate the periods of a spring set in harmonic motion. I observed a period to be .33 s which I later calculated to be .20 s which gave me a percent error of 40. I observed a period to be .47 s which I later calculated to be .28 s which gave me a percent error of 40 also. I observed a period of .52 s and later calculated it to be .40 s which gave me a percent error of 23. The concept, simple harmonic motion, was demonstrated in this lab because throughout it I had to set a spring into simple harmonic motion numerous times while collect data and later performed an analysis. In my analysis I had to find several spring constants, for example 49 N/m for the first mass, which I was only able to find because of the fact that the spring was in simple harmonic motion. My force of gravity vs. displacement graph supports this conclusion because the spring constant can be found, which can only be found if the spring is indeed in simple harmonic motion, by observation of the graph’s slope. By also calculating the spring constant by using Hooke’s Law, which only works when in simple harmonic motion, I can also find the spring constant by calculation and get the same answer. This would allow me to conclude that my graphs demonstrate the concept, simple harmonic motion. My results are consistent with my classmates. I observed in my analysis that when I increased my mass by a lot that my percent error went down. So I can conclude form this observation that this experiment can be improved by using larger masses, sense according to my analysis, produce smaller percent errors.
Questions
1. When I performed step three in the procedure I found that when I pulled the mass spring system down 4.0 cm from the equilibrium position with mass that it went past this equilibrium position 4.0 cm. For every single different mass that was used to conduct this experiment the same thing also occurred.
2.
a.
3.
4. Of course the mass of the stand matters. The mass of everything attached to the end of the spring maters sense it’s connected to the end of the spring which makes it a variable in its simple harmonic motion. The mass of the stand must be added to the mass of the mass. When you find the spring constant, k, you must also factor in the force of gravity on the mass. When you change the mass this value changes which changes you spring constant which also changes the period if you use the formula I used to calculate it. This allows me to conclude that the mass does actually matter sense changing it would change everything I calculated in my analysis.
5. Stiffer springs that only compress a couple of centimeters under thousands of Newton’s of force have higher spring constants because they are “stiffer” and have high spring constants. If the springs in my care were replaced with very stiff springs my car wouldn’t vibrate as freely as softer springs with lower constants. Sense I would have high spring constants the amplitude and period of motion would also decrease and my car would bounce less freely because of this increase in the spring constant.
Dylan,
Could you confirm to me what is the role of the stand in the set-up.
Does it only support the spring and the ruler? If this is the case, then the stand does NOT move with the mass, and thus there is no need to add the mass of the stand in the calculations.
Please kindly confirm.
Also, in my days for physics lab, I record raw data in a separate section called "observations". If I made the same measurements ten times, I would record those readings, instead of reporting just the average. The reason is that in retrospect, sometimes we may want to interpret the data in a different orientation. Raw data allows us to do that.
It is more elegant and less error-prone if you could do the calculations in a table form, for example, for the repetitive calculations for the 3 different masses. A sample calculation prior to the table is perfectly OK.
In the graph for displacement vs force of gravity.
I would put the force of gravity as the independent variable, and the displacement in the y-axis. It is not correct to plot using a non-linear scale (displacement) when the expected behaviour (Hookes law) is linear.
Dimensional analysis:
The paragraph on the checking of formulae using units is excellent. You could devise a paragraph heading for it.
The spring constant appears to vary considerably with the mass. This is not normal. As explained abov, if the "stand" does not oscillate with the mass, the mass of the stand should not be included in the calcultions.
Will continue tomorrow.
Bob has posted this yesterday, don't know if you have taken a good look at it. It contain everything you need to answer question 2.
I will elaborate a little if that would help.
Also, from reading in detail the question, it seems that I have erred in the definition of amplitude. There are certain cases where amplitude is used to mean the difference between the extremes, but in the case of simple harmonic motion, amplitude means the distance from stationary position to the extreme, as given by A in the equation
x=A sin(wt). Sorry if I caused inconvenience.
Let
A=amplitude (max. distance from equilibrium position)
k=spring constant
m=mass
Assume the datum for gravitational potential energy (PE) is at the stretched (lowest) position.
2a. Energy of system (conserved)
PE (gravity) = 0 since it is at datum
PE (spring) = kA since spring is stretched through a distance of A
2b. Velocity v at equilibrium point
At this position,
PE (gravity) = mgA (A above datum)
PE (spring) = 0 (equilibrium position, stretching due to weight is balanced by PE gravity)
Kinetic Energy (KE) = 0.5 m v2
Equating energies at this position with those of the system (case 2a), the velocity can be found.
2c At half-amplitude (A/2 below equilibrium point)
Let
v = velocity of the mass
then
PE (gravity) = mg(A/2)
PE (spring) = k(A/2)
KE = 0.5 m v2
2d velocity at half-amplitude
Equate energies in 2c with those of 2a, the unknown velocity v can be found.
Please add to energies of case 2a:
KE (kinetic energy) = 0
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