Nii-forcesLab

15 Jul Nii-forcesLab

2-Dimensional Forces

Experiment objectives:

1. Achieve an understanding of the vector nature of forces

2. Learn vector algebra with force vector addition/subtraction

3. Cultivate the habit of keeping all experimental data in a well-organized manner

Experiment introduction:

Force vector

Vectors are quantities with directions. Force and velocity are good examples of vectors. When dealing with a vector in physics, one needs to take care of the direction. For example, as shown in

Figure 1, there are two forces, 𝐹⃗1 and 𝐹⃗2, acting on a block. 𝐹⃗2 is 10N pointing in the −𝑥 direction; 𝐹⃗1 is 15N pointing at 𝜃 = 40° above the +𝑥 direction. If one needs to determine the net force, one has to break down the force vectors into their 𝑥 and 𝑦 components first. In this case, 𝐹⃗2 = −10N𝑥̂. For 𝐹⃗1, the following calculation can be used:

𝐹⃗1 = 𝐹1,𝑥 𝑥̂ + 𝐹1,𝑦 𝑦̂

⇓

𝐹1,𝑥= 𝐹1 cos(𝜃)} ⇒ {𝐹1,𝑥 = 15cos(40°) = 11.5N (1)

𝐹1,𝑦= 𝐹1 sin(𝜃) 𝐹1,𝑦 = 15 sin(40°) = 9.64N

⇓

𝐹⃗1 = 11.5N 𝑥̂ + 9.64N 𝑦̂

Please note that the calculation follows the convention that a vector has an arrow on top of the symbol, and the magnitude of a vector has the symbol without the arrow. For example, 𝐹⃗1 is a force vector; 𝐹1 is the magnitude of it. You are expected to follow the same convention.

x y 𝐹 ⃗ 1 𝐹 ⃗ 2 𝐹 1 , 𝑥 𝐹 1 , 𝑦 𝜃

Figure 1: Forces on a block. To facilitate addition/subtraction of forces, the forces which do not line up with either 𝑥 or 𝑦 , in this case 𝐹⃗1, must be broken down to their components.

With the two forces in component form, 𝐹⃗1 = 11.5N 𝑥̂ + 9.64N 𝑦̂ and 𝐹⃗2 = −10N 𝑥̂, the net force on the box can be determined with vector addition, 𝐹⃗total = 𝐹⃗1 + 𝐹⃗2 = (11.5N 𝑥̂ + 9.64N 𝑦̂) + (−10N 𝑥̂) = 1.5N 𝑥̂ + 9.64N 𝑦̂.

Equilibrium

In the study of motion and mechanics, equilibrium refers to the state of motion that the net force on an object is zero. Please note that “being in equilibrium” does not necessarily mean “being stationary”; an object moving with a constant velocity is in equilibrium because it undergoes no acceleration, which in turn means there is no net force on it.

Please also note that the phrase “the net force on an object is zero” may refer to the following two different situations:

1. There is simply no force at all acting on the object.

2. There are multiple forces acting on the object, but they balance each other out. This situation happens very often.

Exploration:

During the Exploration, conduct the following investigation:

1. Pick at least two of the following force combinations, and then use calculation and experimentation to determine the force 𝐹⃗4, both magnitude and direction, to balance the other three forces.

2. Compare your calculation and experiments

Combination	𝐹⃗1	𝐹⃗2	𝐹⃗3
1	1.2~1.5N at 34°	0.7~1.1N at 144°	1.5~1.9N at 203°
2	0.4~0.8N at 0°	1.0~1.4N at 84°	1.2~1.6N at 160°
3	0.7~1.1N at 50°	0.7~1.1N at 90°	0.7~1.1N at 100°
4	0.6~1.0N at 345°	1.3~1.7N at 82°	1.5~1.9N at 200°

Exploration grade: 20 points

Please answer the following questions with one or two sentences. Some of the questions may appear in the post-lab quiz. Your instructor will randomly check your answers.

1. After you balance all forces, how much additional force can you add/subtract from one force to still keep it in equilibrium?

2. After you balance all forces, how many degrees can you move a force to still keep it in equilibrium?

3. How will the issues in the two questions above affect your results?

Please also present the following to your instructor for a grade:

1. Your choice of force combinations

2. 𝐹⃗4 obtained by both calculation and experiments

3. Percent difference of magnitude and angle for measured and calculated 𝐹⃗4 4.Relevant calculation

measured − calculated

%difference = ×100%

calculated

Please note that points will NOT be marked down if any of the above is wrong; however, points will be deducted based on the following guideline.

-10	-5	No deduction
More than half of the materials are missing, illegible and/or poorly organized; results cannot be understood.	Some but less than half of the materials are missing, illegible and/or poorly organized; efforts have to be made to understand the results.	Everything is legible and well organized; instructors can easily understand the results.

Exploration notes:

The figure below shows the force table with hanging masses used in this experiment. Adjusting the weight and position of the hanging masses allows one to balance all forces.	When all forces are balanced, the ring attached to the hanging masses will be centered on, but not in contact with, the metal post at the center of the force table. The angle marks on the table can also be seen.
Hanging masses	Small mass chips, which can be used to answer question 1.
Please note that there are two sets of angle reading O ne may choose either set as long as one stay s consistent.s on the force table, the inner and outer.	Please note that when reading the angle for a string tension force one should only look at the angle mark the string lines up with. It’s a common mistake to use the red mark on the pulley mount to read for angle, but the string is the only true reading.

Application:

For the Application part of this lab, your instructor will assign your group two unknown masses. Please use experimentation and calculation to determine their masses. It is highly recommended that you use only one known hanging mass to find the two unknown ones. Preliminary test shows using one mass, rather than two or more, can reduce calculation and improve results accuracy.

Inform your instructor once you have confidently determined the masses. Your instructor will compare your results to the true masses and determine your Application grade.

Application Grade: 20 points

Please present the following to your instructor for your Application grade.

1. A sketch of the force directions

2. Measured data

3. Relevant calculation

4. Determined masses

		Unknown mass 1
Calculated mass 1 is within ____ of the true value.	≤ ±2.5%	≤ ±3%	≤ ±3.5%	≤ ±4%	≤ ±4.5%	> ±5%
Points	10	8.5	7	5.5	4	2.5
		Unknown mass 2
Calculated mass 2 is within ____ of the true value.	≤ ±2.5%	≤ ±3%	≤ ±3.5%	≤ ±4%	≤ ±4.5%	> ±5%
Points	10	8.5	7	5.5	4	2.5

Additionally, points will be deducted based on the guideline below.

-10	-5	No deduction
More than half of the materials are missing, illegible and/or poorly organized; results cannot be understood.	Some but less than half of the materials are missing, illegible and/or poorly organized; efforts have to be made to understand the results.	Everything is legible and well organized; instructors can easily understand the results.

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Lab 5 Report – Table

Using table is a convenient technique to organize, present and analyze information. When used correctly, tables can help the reader quickly understand abstract concepts, trends, etc. hidden with the information. Please refer to the sample table on the next page.

Requirements:

In this report, please make one data table to present your experiment data for all force combinations you worked on in the Exploration part. Please think about how to organize the data in the table so that it is easy for readers to follow the data and easy for the important information to stand out (the percent errors between the measured and calculated values are the important information in this case). Format

Item	0 points	2 points
Requirements	The requirements above are neglected.	The requirements above are met.
Table title and numbering	Table title and numbering are missing	Table title and correct numbering are presented.
Font format	Non-standard font	Times New Roman font in size 11 and bold type face is used for title numbering; Regular Times New Roman font in size 11 for everything else.

Content

Item	0 points	2 points
Table title content	Table title is missing, or does not describe what the data are.	Table title briefly and clearly summarizes what data are presented.
Table Header	Table header missing	Table header for each row or column are presented to show the meaning of the numbers.
Units in table header	Units are missing even when applicable.	Appropriate units, when applicable, are presented.
Data to be presented: magnitude and direction of all forces in each combination, percent error between measured and calculated 𝐹⃗4 (8 points)	All data are missing.	All data are presented in a well-organized way.

Don’t forget to attach a copy of this rubric to your lab report, otherwise 5 points will be marked down.

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Sample Table

A sample table is given below.

Obviously, the sample data and the lab data are different, you may consider using the sample table as a starting point to build your own, but simply “copy and paste” will not fit well.

Table 1: Comparison of the Gross Domestic Production ( GDP ) growth for the USA and China from 2008 to 2013 Year GDP (Trillion $) China USA 2008 4.52 14.3 2013 9.83 16.8 % growth % 117 % 17.4 Table numbering and title; the title summarizes what the data are. Table header of columns and rows, and units when applicable.

This table presents data in an uncluttered manner, and highlights the different % growth of both countries by placing the two numbers side by side.

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DATA