Physics 221

Write the names, title, objectives, and relevant equations section.Do not tape the procedure or equipment sections. You will be writing the procedure as you perform the lab, as well as updating the equipment list and taking data. Your notebook will be checked off during lab, and the photocopy of the pages is due on Thursday, October 27.

Lab 4: Finding the tension force of a cart on a ramp

Objectives:

• Calibrating a digital force sensor

• Measuring the force exerted by a stationary cart on a ramp at five different angles

• Comparing the measured value of the force to the theoretical value of the force

• Writing and illustrating an equipment list for a laboratory exercise

• Writing a laboratory procedure that other students may follow

Introduction and relevant equations:

Newton’s second law states that the force is proportional to both the mass of the object the force is impressed upon and the consequent acceleration of the object.

(Draw a free-body diagram showing all of the forces acting on the cart. Label all of the forces with the appropriate vector).

(Further, set up an appropriate coordinate axes to analyze the net force acting on this cart, and then write the two equations that show the forces acting in the x and y directions).

Equipment:

•collision cart with force sensor attachment

• Vernier Dual Range Force Sensor

(Complete the list of equipment, using brand or manufacturer names where appropriate)

(Photograph or sketch of the setup. Label the various parts of the apparatus.)

Procedure: (The goal of this section is to write a procedure that may be given to any other team in the class, and they should be able to recreate your experiment)

Calibrating the force sensor

(Write at least three steps you used to calibrate the force sensor. Note that you should have the force sensor setting on “10 N”. Consider how you would show that a force of 9.81 N was acting on the sensor?)

Measuring the force exerted by the cart

(Examine the photographs below and mimic the setup; note that some of the equipment you will use is different. Write at least five steps you used to measure the force exerted by the cart at five different ramp angles. The last run should be at a 90° inclination. The force sensor setting should still be on “10 N”. One big hint: instead of our usual rule about “1 in the last digit”, use the “play” function on the datalogger to record 10 force measurements over a few seconds, then calculate the mean and standard deviation (which is a better measure of uncertainty anyway).)

Data and preliminary analysis:

(What masses must be weighed and recorded?) (What is the uncertainty in the mass?)

(Set up a data table like the one below)

Run number / Angle of incline (°) / Measured force on cart by string (N) / Theoretical force on cart by string and its uncertainty (N) / Percent error
Mean / Std. dev.
1
2
3
4
5 / 90°

Reality check: How many significant figures should each column have, including the mean and standard deviations?

Analysis and results:

Calculate the force that should be exerted by the string on the cart (the theoretical force), using the free body diagram set up in the “Relevant equations” section. Fill in the appropriate column on the previous table.

Show one of these calculations in this section of the notebook. Clearly state the value of g you are using, and its source (full citation).

Assume the value of g has an uncertainty of “1” in its last digit, then calculate the uncertainty in the theoretical value of the force. Show the setup of this calculation for one of the rows.

Calculate the percent error between your mean measured force and the theoretical force. Show one of these calculations clearly.

Discussion

1. Why did the string that connects the cart and the top of the ramp need to be parallel to the ramp surface? In other words, what free-body diagram-related assumption was satisfied by making the string and the ramp surface parallel?

2. Why were “10 force measurements over a few seconds” taken for each run? Hint: there are two reasons.

Conclusion

3. Suppose someone claims that we did not take into account ramp friction, and thus friction is the most significant source of error in this experiment. How do the results of your final run support or contradict this claim?

4. Were the “theory” predictions of force consistent with the measured force? How can you tell?