Newton’s Second Law of Motion
Overview
The purpose of this investigation
is to validate
Force, mass,
and acceleration all must be measured in order to complete this lab.
Force data is collected by calculating the weight of the calibrated mass(es) on the end of the string
(and the resulting tension in the string for Part A). Mass data is
collected with a triple beam balance. Acceleration data is collected by a
CBR sonic ranging device working in connection with Logger Pro software running
on a Windows computer. The CBR is connected to Port 2 on the Universal
Lab Interface (ULI). The ULI is connected to the serial port on the
computer. The CBR is then enabled to send distance and time data to the
computer. The Logger Pro program stores, graphs, and analyzes this
numerical data allowing the user to determine velocity, acceleration, etc.
In this section of the lab, a lab cart of constant mass is pulled by a weight hanging on a string that passes over a pulley. By changing the weight at the end of the string, different amounts of force can be applied to the object. It is important to realize that it is the tension in the string that is causing the cart to accelerate.
1. Do not turn on the computer until the following connections are made: connect the ULI to the serial input on the back of the computer, connect the CBR to Port 2 on the front of the ULI, and plug in the power supply for the ULI. Only after all connections are made, turn on both the computer and the ULI (the CBR has no switch).
2. Complete the mass data table using the triple beam balance.
3. The Logger Pro program must be opened with the file called Velocity vs Time. The CBR should be connected to Port 2 on the interface box. When the Collect button is clicked the CBR will soon begin collecting data.
4. Attach the string to the cart and pass it over the pulley but hang nothing on the end. Click Collect, wait until you hear the clicking of the CBR, then pull the cart away from the CBR and let it coast to a stop. (This is a measure of the friction acting on the cart.)
5. You should now be looking at a graph of velocity vs. time that clearly shows the object at rest, the object accelerating, and the object decelerating. If not, you need to repeat the experiment – simply click on the Collect button to repeat. You may need to adjust the direction the CBR is pointing if it is getting errant reflections (normally it works best when tilted slightly upward).
6. You now need to get the acceleration of the cart as friction slowed it. To do this, click and drag across the region of the graph that you want to measure (the part where the cart was slowing down). Highlight only the linear portion.
7. Now we want to do a best fit or regression. Click on the tool bar button labeled with a capital R in order to get a linear regression of the selected part of the graph.
8. If all seems well with the regression, then record the results in the data table (on the row marked “none”), making sure to include units in the spaces provided. The line of best fit should match the data very closely! The correlation coefficient is an indicator of how well the data matches the best fit: the closer R is to 1 the better the match. The computer labels this as Cor; it is also often called simply R. It should be possible to get values of R of at least 0.990 – if it is less than this, then try selecting a more narrow part of the graph or do the trial again if you feel like you have enough time.
9. Now, attach one end of the string to the lab cart. The string passes over the pulley, which is mounted at one end of the lab table. At the other end hang a mass of 20 g. When the cart is released it will accelerate – catch the cart before it gets to the end and before the hanging mass hits the floor!
10. Use the steps explained above to collect data concerning the acceleration – being careful to select the part of the graph that corresponds to the object being pulled by the weight, this time the part where its speed is increasing.
11. Repeat the process for masses of 40 g, 60 g, 80 g, and so on until the table is complete and you have seven unique values of acceleration.
In this section of the lab a cart will begin with no mass loaded onto it. Then under the influence of the same force each time, increasing amounts of mass will be loaded onto the cart. In order to negate the effect of friction the cart will roll on a slight incline. In this part of the lab, all masses will be treated as one accelerating system of masses.
1. Before attaching the string to the cart, adjust the height of the ramp until the cart will roll down it at a constant speed (after a slight push to get it started). When the ramp is tilted just enough the effect of friction is negated by a component of gravity and the net force on the cart is zero.
2. Attach one end of the string to the cart, pass it over the pulley, and hang a 50 g mass from the other end. This same mass will hang on the string and provide the same force for each trial. Record this value in the mass table.
3. Use the program to collect, graph, scrutinize, and record acceleration data just as explained in part A.
4. Repeat the process with 200 g, 400 g, 600 g, 800 g, and 1000 g of mass placed on top of the cart. Do not change the mass pulling the cart. In this way you are changing the mass being accelerated without changing the amount of force.
1. Complete the bottom table on the data sheet for part
A: Acceleration is simply copied from the regression results.
Determine the tension in the string (in newtons) for
each trial. Be careful – the tension is not equal to the gravity
acting on the hanging mass (when accelerating). You must use
2. Use these results to construct a tension vs. acceleration graph. For this graph only, plot the independent variable (tension) on the y-axis. Determine the line of best fit and its equation.
1. Complete the bottom table on the data sheet for part B: Total mass being accelerated includes the cart, the string, and all other masses that accelerated with the cart, including the one on the end of the string. Calculate the reciprocal of this. Acceleration is simply copied from the regression results.
2. Use these results to construct an acceleration vs. mass graph. Draw the best fit. Determine the equation assuming this to be a hyperbola of the form: y = k/x. Calculate k using each datum, find the mean value of k, plot the resulting curve. Show your work on the graph.
3. Also construct a “curve straightening” graph of acceleration vs. mass –1. On this graph the x-variable is the reciprocal of the total mass being accelerated. Determine the line of best fit and its equation.
A complete report (50 pts): (5 or 6 pages in this order)
q Completed data/results tables. (6)
q Tension vs. Acceleration graph. (10)
q Acceleration vs. Mass graph. (10)
q Acceleration vs. Mass –1 graph. (10)
q On separate paper, responses to the questions. (14)
1. Show one example of how you calculated the tension in the string based on the hanging mass and its acceleration.
2. Discuss whether or not your graphs confirm and/or
support the types of relations described in
3. Consider the line of best fit for the graph of Tension vs. Acceleration. (a) What does the slope represent? (i.e. it should be equal to what?) Explain your answer. (b) Assuming the values on your data sheet are accurate, calculate the percent error in the slope value. Show your work. (c) What does the y-intercept represent on this graph? Explain.
4. In Part B the track was tilted to counteract friction. When additional mass was added to the cart, was friction still counteracted correctly by the track tilted the same amount? Explain and/or support your answer. Hint: you may want to try solving for the acceleration of the cart symbolically.
5. Consider the value of the constant k from the
graph of Acceleration vs.
6. Consider the line of best fit for the graph of Acceleration vs. Reciprocal Mass. (a) What does the slope represent? (i.e. it should be equal to what?) Explain your answer. (b) Assuming the values on your data sheet are accurate, calculate the percent error in the slope value. Show your work.
7. Discuss error in this lab. (Things to discuss: indications and signs of error – random and/or systematic, the probable and significant cause(s) of the error that is apparent in the results. The goal of discussing error is to explain satisfactorily why the results of your lab are not quite exactly what was expected. Be as specific as possible. You will almost always have unexpected results in an experiment. Your task is to write a discussion that is intelligent, thoughtful, and insightful!)
Part A – Acceleration vs. Force
mass of cart |
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mass of string |
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Results of CBR/Logger Pro linear regression of velocity-time graph: |
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mass on end of string |
Slope ( ) |
y-intercept ( ) |
Corr. Coeff. (no units) |
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none |
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20.0 g |
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40.0 g |
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60.0 g |
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80.0 g |
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100.0 g |
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150.0 g |
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mass on end of string |
Tension in string (N) |
Acceleration (m/s2) |
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none |
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20.0 g |
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40.0 g |
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60.0 g |
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80.0 g |
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100.0 g |
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150.0 g |
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Mass of cart and string |
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Mass on end of string |
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Results of CBR/Logger Pro linear regression of velocity-time graph: |
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Mass added to cart(g) |
Slope ( ) |
y-intercept ( ) |
Corr. Coeff. (no units) |
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0 |
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200 |
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400 |
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600 |
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800 |
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1000 |
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Total mass being accelerated: m (kg) |
Reciprocal of total mass being accelerated: 1/m (kg –1) |
Acceleration obtained from regression: a (m/s2) |
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