NCSU Physics - Labs for Sci. & Eng. - Mechanics 4 (Homework)

James Finch

Physics - College, section 1, Fall 2019

Instructor: Dr. Friendly

Current Score : 0 / 45

Due : Monday, January 28, 2030 00:00 EST

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1	2	3	4
–/4	–/2	–/1	–/38

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0/45 (0.0%)

Instructions
The Inlab assignment below is a sample from Physics Labs for Scientists and Engineers - Mechanics, 4th edition from the NC State University Physics Department. This assignment demonstrates some of the key features of this lab course, including the following.
- background discussion with Concept Check questions
- embedded videos to demonstrate experimental setup
- experimental procedure, data collection, and analysis all integrated into the assignment
This demo assignment allows many submissions and allows you to try another version of the same question for practice wherever the problem has randomized values.

Assignment Submission

For this assignment, you submit answers by question parts. The number of submissions remaining for each question part only changes if you submit or change the answer.

Assignment Scoring

Your last submission is used for your score.

1. –/4 points NCSUCalcPhysMechL4 4.LR.001. My Notes

Group Roles

Before you start the lab, identify who on your team will assume roles shown below. In any unused spaces, enter "none" to receive full credit for this question.

If necessary, read the descriptions of Group Roles for Labs.

Lab Manager Recorder Skeptic Energizer (optional)

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2. –/2 points NCSUCalcPhysMechL4 4.IL.001. My Notes

Lab 4: Uniform Circular Motion

Background

Background

Figure 1

Various types of motion can be approximated as uniform circular motion—a car rounding a curve, for example, or a planet in a nearly circular orbit.

In the first portion of this lab, you will determine the mass of a rubber stopper by attaching a string with a weight to it, swinging it over your head and measuring the radius of the arc as well as the period of the swing, as shown in the animation above.

The principle behind this experiment is that the weight of the hanging mass (m_h) provides a tension that will provide the centripetal force for the swinging mass.
Concept Check!

Concept Check!

Consider a mass such as a rubber stopper (M_s) moving in a horizontal arc, as shown in the animation above.

Which one of the following equations is an expression for the centripetal force on the stopper?

M_s
v²
r

m_h
v
r²

m_h
v²
r

M_s
v
r²

This centripetal force on the rubber stopper is also equal to the force on the hanging mass.

m_h g

The speed of the moving mass can be related to the period of rotation and the radius of the path. Since speed is distance over time for constant speed, the distance of a circular path (the circumference, 2πr) divided by the time to travel the path (the period, T) gives the following speed.

v =
2πr
T

Thus, the centripetal acceleration, a_c can be written as the following.

a_c =
v²
r
=
4π²r
T²

Then, the centripetal force, F_c, provides the tension (F_T) in the cord.

Given the above, which of the following are equivalent expressions for the magnitude of the tension force? Select all that apply. (Hint: Draw a picture of the apparatus, and label the forces acting on the two masses.)

F_c

M_s
v²
r

M_s
4π²r
T²

m_h g

In the second part of the lab, you will also account for the force of gravity on the rubber stopper to ensure that all forces are accounted for. You will use Tracker software to determine the angle of interest.

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3. –/1 points NCSUCalcPhysMechL4 4.IL.002. My Notes

Setup

Setup

Most of the data collection from the lab will involve the following method.

1.

Cut a long piece of string and run it through the steel tube so it sticks out both sides.

2.

Tie the rubber stopper to the end of the string on the side of the tube with the white plug. (This is a Teflon plug designed to reduce friction.)

3.

Tie a loop at the other end of the string. You will hang the mass hanger from this end.

4.

To achieve uniform circular motion, hold the tube vertically with the mass hanger (shown in gold below) at the bottom and spin the stopper (shown in black below) around in a circular motion.

Figure 2: The Uniform Circular Motion apparatus
TA Checkpoint!

TA Checkpoint!

Before moving on, ask your TA to check your work and enter the code word here.

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4. –/38 points NCSUCalcPhysMechL4 4.IL.003. My Notes

Question Part

Points

Submissions Used

–/1

0/100

Total

–/38

Use the exact values you enter to make later calculations.

Procedure and Analysis

Be very careful during this lab to avoid hitting any other objects (or people!) with the rubber stopper!

To measure the period, perform the following.

Use a timing device (such as your smartphone's stopwatch) to record the time for 10 full oscillations.

Divide the total time for the 10 oscillations by 10 to determine the average period of rotation, T. Measuring for 10 oscillations is done to minimize the effect of measurement uncertainty.

To measure mass and arc radius, perform the following.

To determine L, the arc radius: When you're ready to stop spinning the stopper, grab the string so that you can measure its length without it sliding.

To determine the masses: Weigh your hanging weights on the scale to determine m_h. That way, you can account for any chips or scratches in your weights.

Continue taking data using a variety of hanging masses. Record your data in the table below.

Table 1
Trial	T (s)	L (m)	m_h (kg)
1
2
3
4
5

Experimental Determination of Mass – Calculations

An Alternate Method – Data and Calculations

An Alternate Method – Data and Calculations

Perform one more trial, making sure that you have a way of determining the angle, θ.

In Part 1, we said that the only force acting on the stopper is the tension in the string, and so the tension equals the centripetal force. In reality, gravity also acts on the stopper.

The string will actually be at an angle, as shown in Fig. 3, rather than purely horizontal. In this case, the tension force (calculated with
m_hg),
is the hypotenuse of a right triangle, where the vertical side is the gravitational force on the stopper
(M_sg)
and the horizontal component is the centripetal part

M_s
v²
r
.

This means that when you include gravity, the centripetal force term (
M_s a_c
) is actually equal to only the horizontal component of the tension,
m_h g cos(θ),
so that we have the following.

M_s a_c = m_h g cos(θ)

Figure 3: A diagram of the Uniform Circular Motion apparatus that includes forces.

1.

Perform one more trial, making sure that you have a way of determining the angle, θ. Record the period (in s), radius (in m), and the mass (in kg) of the hanger.

T = s L = m m_h = kg

2.

What is the magnitude of the angle (in degrees) formed by the string relative to the horizontal during this trial?

°

3.

Based on this angle, what is the mass (in kg) of the stopper?

M_s = kg
Analysis

Analysis

What is the percent difference between the two values of M_s?

%

What factors may contribute to the difference in these two values?

This answer has not been graded yet.

Based on the assumptions made and possible sources of error, as well as the accuracy of the data collection methods, which value do you feel is likely to be more accurate? Why?

This answer has not been graded yet.

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Table 2
Trial	a_c (m/s²)	m_hg (N)
1
2
3
4
5

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NCSU Physics - Labs for Sci. & Eng. - Mechanics 4 (Homework)

Current Score : 0 / 45

Due : Monday, January 28, 2030 00:00 EST

Last Saved : n/a Saving... ()

Instructions

Assignment Submission

Assignment Scoring

Group Roles

Lab 4: Uniform Circular Motion

Background

Background

Concept Check!

Concept Check!

Setup

Setup

TA Checkpoint!

TA Checkpoint!

Procedure and Analysis

Procedure and Analysis

Experimental Determination of Mass – Calculations

Experimental Determination of Mass – Calculations

An Alternate Method – Data and Calculations

An Alternate Method – Data and Calculations

Analysis

Analysis