Dynamics and Forces Lab

Objectives

  • Experimentally study Newton's second law of motion.
  • Verify that the relationship between Force and Acceleration is linear.

Physics Overview

At the very heart of describing the motion of objects is the study of what causes objects to move. This field is called dynamics. In classical mechanics, forces are fundamental agents causing motion. Sir Isaac Newton first formulated what are now called Newton's Laws of Motion. Of these, the second law of motion, is arguably, one of the most well-known equations in science. The essence of the second law of motion can be stated as:


"The acceleration of an object is directly proportional to the net force acting on it and is inversely proportional to its mass. The direction of the acceleration is in the direction of the net force acting on the object."


Thus, if an object of mass \(m\) experiences a net force \(\vec{F}_{net}\) then it experiences an acceleration such that:


\[ \vec{a} \propto \vec{F}_{net}. \label{eq:Newton2_1}\]


Thus the magnitude of the acceleration is proportional to the magnitude of the net force and the direction of the acceleration is parallel to the direction of the net force.


The constant of proportionality is the inverse value of the mass. Hence Newton's second law can be written as,

\[ \vec{a} = \frac{1}{m}\vec{F}_{net}, \label{eq:Newton2_2}\]


which yields the familiar relationship:

\[ \vec{F}_{net} = m\vec{a}. \label{eq:Newton2_3}\]


This also implies that, given a particular force, there is a linear relationship between the force and the acceleration, and the slope is the mass of the object. This is what we will be exploring in this lab.


If you would like to get a quick refresher about Newton's Laws of motion, see the following video.



Apparatus

For carrying out the experiment you will need the following equipment:

  • iOLab Device and corresponding USB Dongle.
  • iOLab accessory kit.
  • Physics 200L lab kit

Give it a go!

give it a go

Procedure

The procedure to be followed for doing the experiment is given below. There are three parts to this lab; Part I, Part II and Part III.


Part - I (Determine the mass of the iOLab Device):


Here is a video that shows how to do the experiment to determine the mass of the iOLab device.


This is the procedure to be followed:

  1. Attach the screw from the accesory kit to the bottom of the iOLab Device.
  2. Place the device upside down on the table; the \(y-\)axis of the device should point downwards.
  3. Turn on the device and and open the data collection software on your computer after plugging in the USB dongle. On the software select both the force sensor as well as the accelerometer.
  4. With the iOLab device still sitting on the table, press record and collect data for about \(10\)s.
  5. Now while the data is still getting recorded, holding the screw, lift up the iOLab device and hold steady for about \(10\)s, then place the device back on the table and record data for another \(10\)s.
  6. Find the average values of the force and acceleration when the device is sitting on the table and when the device is lifted. Subtract the average value of the force when the device is on the table from the average value of the force when the device is lifted. Dividing the result by the average value for the acceleration in the \(y-\)direction will give you the mass of the device using Newton's second law.


Part - II (Determining the relationship between force and acceleration):


The video below shows what you will be doing in this part of the experiment.

The procedure is as follows:


  1. First remove the screw and attach the little plate from the iOLab accessory kit to the iOLab Device.
  2. Turn on the iOLab device and open the data collection software on your computer after plugging in the USB dongle. Now select both the force sensor and the accelerometer probes.
  3. Place the iOLab device on its back; i.e., with the wheels facing up, start recording data and give the device five consecutive pushes (see video above for a demo) of increasing strength. Stop recording data after the final push.
  4. Hover your mouse over the peaks on the force and acceleration data. Record the value for each peak.
  5. In Excel make a data table of the peak values of Force and peak values of acceleration. Make a plot of force vs acceleration using this data. Add a linear trendline and display the equation on the chart. The slope is the experimentally determined value for the mass of the iOLab device.
  6. Compare this value to the mass you determined using Part I.


Part - III (Time varying force):


The video below shows what you will be doing in this part of the experiment.

The procedure is as follows:


  1. First remove the little plate and attach the screw and to the screw attach the long spring from the iOLab accessory kit.
  2. Thread screwdriver from the Physics 200 lab kit through the other end of the spring.
  3. Place the screwdriver on the edge of the table, such that only a quarter of its length jutts over the edge. Now place a bunch of textbooks on top of the screwdriver on the table so that the iOLab device is suspended over the edge of the table as seen in the video above. Allow the device to hang and dampen out any residual oscillations.
  4. Once the device is stationary, turn on the device and the on the data collection software select both the force sensor and the accelerometer probes.
  5. Now pull the device downwards slightly and allow it to oscillate vertically.
  6. On the data collection software make a parametric plot of acceleration vs force as seen in the video above. Determine the slope of the plot which is related to the mass.
  7. Compare this value to the values of the mass you determined in Part I and Part II. How do the three compare?

Report Considerations

Make sure you include the following in your lab report:

  • Include ONE (1) example snapshot showing your analysis of the peaks of the force and acceleration data.
  • Include ONE (1) data table of the peaks of the force and acceleration. Include units.
  • Include ONE (1) plot of the force vs acceleration data from Part II above.
  • Include ONE (1) parametric plot of the acceleration vs force data from Part III above.
  • Be sure to include explanations of how you calculated the slopes in Parts II and III.
Questions to answer in the discussion section.
  • What can you say about the errors in your experiment?
  • How do the values for the mass determined in Part I, Part II and Part III compare?