lab report

LABREPORTNewtons2ndLaw-PHY241-Medvar.docx

Newton’s Second Law of Motion

Physics 231

At the end of the lab experiment please clean your table and wait for the instructor to check you out! All the group partners must be present. Thank you.

Equipment:

Bubble level (on front bench)	Collision Cart
Track · feet · end stop · super pulley with clamp	Weight holders – paper clips
	Weights
	Wireless Motion Sensor
	Electronic balance, 600-g capacity

Objectives:

· Verify Newton’s Second Law of Motion

· Determine a value for the acceleration of gravity (g)

Background:

Consider the set-up described in the figure below: the mass of the cart (M) is allowed to move on a frictionless surface (dynamic track) while being pulled by a mass (m) hanging from a string attached to the cart and supported by a frictionless pulley.

An analysis of this system using free-body diagrams and Newton’s second law shows that acceleration (a) of both masses is given by

(m/s2) (1)

i.e. the acceleration of the system is proportional to the hanging mass m.

If the experiment is performed in such a way that the total mass Mt is maintained constant, a graph of the acceleration versus the hanging mass m should be a line with a slope equal to [g / (Mt)], thus, a strong linear relationship between (a) and (m) validates Newton’s second law.

The experiment also provides a method to obtain an estimate of the acceleration due to gravity (g) once the slope of the acceleration versus (m) line has been determined, i.e.

(m/s2) (2)

Set up:

· Slide the end of the track without a bumper into the slot on the front of the motion sensor.

· Turn the motion sensor so that brass screen is facing straight down the track. This screen is the actual sensor. Turn on the sensor by hitting the power button on the side of the sensor.

Attach the black super pulley to the opposite end of the track from the motion sensor, where the solid end stop is located, by putting the flat part of the clamp on the top of the track and tightening the screw up against the bottom of the track.

· Adjust the height of the pulley at the end of the track so that the string pulling the cart is horizontal (parallel to the track). Adjust the height and direction of the sensor so the beam reflects on the cart as it moves down the track.

· Place the collision cart on the track with the string end towards the solid end stop.

· Thread the paper clip, with string attached, through the hole in the end stop and run the string over the pulley.

· The track should be level already however, if your cart will not sit still on the track use the bubble level at the front to check it. If it is no longer level, adjust the feet on the bottom of the track until it is level.

Open the Capstone software and then click on “Sensor Data”. This will open the hardware setup from the menu on the left side of the screen. Select the Wireless Sensor that matches the number on your motion sensor.

· The sensor should be set to record 20 data points per second. To do this, click the down arrow at the bottom of the Capstone screen (see image below) to change it to 20.00 Hz.

Set the graphs to display position, velocity, and acceleration. (You can do this by clicking twice to create two more plots for velocity and acceleration.) You will not need the table, so you can delete it.

Procedure:

· Place five 5-g weights (or any combination of weights totaling 25-g) in the sunken “mass tray” (see picture below) on the top of the cart and attach a 10-g weight at the end of the string (use a paper clip as a hanger not the hanger in the weight set). The total mass M + m referred to in the background discussion includes the mass of the cart with the string and the hanger (paperclip) (M), the five 5-g weights on top of the cart (Mg), and the 10-g hanging weight, (m) = 493.47g. As different experiments are conducted, masses will be transferred from the cart to the hanger and, therefore, the values of (Mg) and (m) will change for each case; (M) - mass of cart, string and hanger will remain constant throughout.

· The cart which will be released from the same position along the track in all experiments, about 15-cm (actual 22cm) in front of the sensor. When releasing the cart, be sure not to give it any push forward. To avoid wobbling of the cart after release, it may be useful to hold the cart from both sides before release and let go from both sides simultaneously or to hold it using a pencil from the side.

· Let the cart go and start recording when the cart appears to move smoothly without “wobbling”; this is usually achieved after about 20-cm of travel from the start. While recording data, a light will be blinking. Stop recording before the hanging mass(es) hit the floor or the cart reaches the end of the track; prevent cart from hitting the end of the track. The total useful recording distance may only be 30 to 40-cm: it is enough to analyze the data.

· Repeat step 3, in case data collection failed or was erratic. Sets of data are referred to as “Run 1”, “Run 2”, etc., in your software. Be sure to record carefully which runs correspond to which amount of hanging mass.

· Remove one of the 5-g weights from the cart and hang it from the end of the string together with the mass(es) already hanging.

· Repeat steps 3 through 5 above for the new distribution of masses until all of your masses are hanging from the string.

Analysis/Discussion/Conclusions:

· After all 5-g weights have been transferred from the cart to the string you are ready to analyze the data on the graphs. Begin with the graphs created from the initial set up of 25-g on the “mass tray” of the cart and 10-g of hanging mass.

· Examine the position graph. Even though there may be oscillations, particularly at the beginning and end of the graph (initial wobble of the cart and/or masses hitting the floor), there usually is a section where position versus time displays the expected trend of a smoothly increasing distance with time. Note the time interval during which this smooth behavior is observed: this is the period of time you will focus on when you derive data from the velocity and acceleration graphs. Select the best of your two runs.

The position graph describes the motion of the cart under constant acceleration. The curve should, therefore be described by the equation x = x0 + v0 t + (1/2) a t2 . Using “Curve Fit” -quadratic determine the best fit line representing the data. The equation provided by Capstone Software if of the form x = At2 + Bt + C. Therefore A (experimental value) should be equal to (1/2)a. Report the value of a = 2A in the appropriate column of the data sheet. This is a first experimental value for the acceleration of the cart.

Run 1 0.0678t^2 + 0.144t + 0.346

A(experimental) = 0.0678

a=2A

a=2(0.0678)

a=0.1356

Run2

· On the velocity versus time graph, highlight the section showing a linear trend (this should appear for the time interval you identified before on the position graph), determine the slope (“Fit”-linear). The slope of the v versus t line is the acceleration of the cart (velocity is linear function of time for motion under constant acceleration and the slope of the v-t line is the acceleration). Report this value of the acceleration in the appropriate column of the data table.

· Run 1 = 0.135t + 0.143

· On the acceleration graph for the same run, highlight the section during which the acceleration appears constant (this should happen for the same time period during which velocity increased linearly). Determine the average value of the acceleration during that period (use the Σ tool). Report this value of the acceleration in the appropriate column of the data table.

· Calculate the average of the two experimental values of the acceleration reported in the data table and report as (aav) in the data table.

· Repeat steps 2-5 for each hanging mass m.

· Draw a graph acceleration (aav) versus hanging mass (m), draw the best fit line and determine the slope and r2 value for this regression line. Discuss whether the acceleration is proportional to the force applied as predicted by Newton’s second law.

· From the slope of the acceleration versus hanging mass graph, use equation (2) above to estimate the value of the acceleration of gravity. Determine the percent error between your experimental value and the accepted value of 9.80 m/s2.

· Discuss possible sources of error during the experiment.

Clean Up:

· Turn of the 850 UI, unplug all cords from it, and put it in the box properly. Use the labeled photo in the lid of the box. Separate the 2 halves of the power cord.

**Do NOT wrap the cord around the box portion of the power cord.**

· Put the half of the power cord containing the box in the back section of the insert and the electrical outlet end of the power cord in the front section of the insert with the USB cable.

· Remove the motion sensor from the track, coil the cord neatly next to the sensor and secure it with the Velcro strap.

**Do NOT wrap the cord around the motion sensor.**

· Remove the cart from the track and return it to the appropriately labeled bag –

**Do NOT remove the string or paper clip from the cart.**

· Remove the super pulley with clamp from the end of the track.

· Return the weights to the boxes in the front of the lab.

Newton’s Second Law of Motion – Data Sheet

Physics 231

Name: Date:

Mass cart, string and hanger: M (kg)

Masses on cart: Mg (kg)

Hanging mass: m (kg)

Total mass: Mt = M + Mg+ m (kg)

Case:	1	2	3	4	5	6
m (kg)	10	15	20	25	30	35
Mg (kg)	25	20	15	10	5	0
M (kg)	493.00	493.00	493.00	493.00	493.00	493.00
Mt (kg)	493.00+35=528	528	528	528	528	528
a (m/s2) (position)	A=0.0678*2 0.1356	A=0.114*2 0.228	A=0.15*2 0.30	A=0.196*2 0.392	A=0.229*2 0.458	A=0.268*2 0.536
a (m/s2) (velocity)	0.135	0.225	0.304	0.384	0.461	0.536
a (m/s2) (acceleration)	0.14	0.23	0.31	0.38	0.47	0.54
aav (m/s2)	0.137	0.228	0.305	0.385	0.463	0.537

lab report

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