Writing Newtons Laws 2 Lab Report
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instruction_1.docxPhysics 161
Newton’s Laws II
Introduction
In this laboratory you will explore a few aspects of Newton's Second Law using Capstone and the Dynamics Track. In Part I, you will use hanging weights to accelerate a cart away from a motion sensor and use the data you record to measure the acceleration of gravity and test Newton's Second Law. In Part II, you will observe the magnitude of the frictional force on an object at rest as well as the force of kinetic friction once that object has been brought to a constant velocity. This will be done indirectly by observing the force needed to accelerate an object at rest to a constant velocity and comparing it to the force needed to maintain a constant velocity.
Reference
Young and Freedman, University Physics, 12th Edition: Chapter 4, section 4.3-4.4, Chapter 5 sections 5.1-5.3
Theory
In this experiment, the force used to accelerate the cart is applied by hanging weights. When the cart is pulled by the hanging weights, the total system (both the cart and the hanging weights system) is accelerated. As a consequence, Newton's Second Law can be written as (ignoring the friction force):
If we define mtotal = mcart + mhang , this can be rewritten as:
By plotting mtotal*a vs. mhang, one can find g as the slope of this plot
Note: To decrease the acceleration of the cart, you will add 500g to the cart, and mcart in these equations will be equal to the measured mass of the cart + added weight. We shall keep that combined mass constant. You will measure the mass of the cart (with the attached force sensor, which is just providing the hook for pulling) using the scale.
Part II: We consider two classes of frictional forces, those for objects at rest (static friction) and those for moving objects (kinetic friction). The force of kinetic friction on a moving object acts in the direction opposite to the velocity of the object. The magnitude of the force of kinetic friction is given by
In the static case, things are slightly more complicated. Similar to Equation 3, we can write:
Procedure
Part I:
1. Make sure the track is level. You can check by making sure that the cart does not roll to one end or the other spontaneously.
2. Measure the mass of the cart plus added weight, convert it to kilograms and record it in Excel in the column mcart. This mass will be constant in our experiment.
3. Connect the motion sensor to the PASCO 850 Universal Interface. In Capstone under Hardware Setup digitally plug in the Motion sensor II from the Sensors menu. Change the Motion sensor’s trigger rate to 50 Hz. Drag a Graph icon into the workspace area and set the y-axis to Velocity.
4. Set the cart on the track at the end closest to the motion sensor. Attach a string to the end of the cart and place it over the pulley. The other end of the string should be connected to the hanging mass of 150 g.
5. One student should hold the cart in place while the other student presses RECORD to collect data in Capstone . You may want to delay releasing the cart for a second in order to make sure you get all the data.
6. Release the cart, being sure to catch the cart before it hits the end of the track, then hit Stop in Capstone.
7. Highlight the points on your graph that follow a straight line (the slope should be positive because the cart is accelerating away from the motion sensor). Do NOT include the end points of this line segment in the data (those values may be affected by forces your hands apply in releasing and stopping the cart.)
8. Using the Linear Fit tool, measure the slope of the velocity graph and record this value (the acceleration) in the table you made in Excel. Your table should have the following information:
Hanging mass mhang(kg)
mcart (includes the added mass) (kg)
Total Mass mtotal (kg)
Acceleration, a (m/s2)
Total Mass * a
F(N)
0.15
0.14
0.13
0.12
0.11
0.10
where mtotal == mcart + mhang
9. Now remove 10 grams of mass from the hanging mass. Perform steps 6-8. If you can, include all the velocity data on the same graph. Remember to record the Total Mass in kilograms!
10. Repeat step 9 until the hanging mass is 100 grams. Once you have recorded all of your mass and acceleration values, calculate the total mass times acceleration of the cart during each run and complete the above table in Excel.
11. Using your data in the table, plot Total mass *a vs. hanging mass . Place a trendline in this plot and find the acceleration of gravity.
12. To find the uncertainty in g, rewrite equation (1) as
