Homework for lab 3 force and motion

Physics Lab 3

3 2-Dimensional Forces

Experiment objectives: 1. Use standard deviation to assess the quality of measurement data 2. Use average and uncertainty to assess reliability of measurement result 3. Distinguish experimental uncertainty from human error 4. Cultivate the habit of keeping all experimental data

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, �⃗�1 and �⃗�2, acting on a block. �⃗�2 is 10N pointing in the −𝑥 direction; �⃗�1 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, �⃗�2 = −10N�̂�. For �⃗�1,

the following calculation can be used:

�⃗�1 = 𝐹1,𝑥 �̂� + 𝐹1,𝑦 �̂�

⇓

𝐹1,𝑥 = 𝐹1 cos(𝜃)

𝐹1,𝑦 = 𝐹1 sin(𝜃) } ⇒ {

𝐹1,𝑥 = 15 cos(40°) = 11.5N

𝐹1,𝑦 = 15 sin(40°) = 9.64N

⇓

�⃗�1 = 11.5N �̂� + 9.64N �̂�

(1)

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, �⃗�1 is a force

vector; 𝐹1 is the magnitude of it. You are expected to follow the same convention.

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 �⃗�1, must be broken down to their components.

x

y

�⃗�1

�⃗�2 𝐹1,𝑥

𝐹1,𝑦

𝜃

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With the two forces in component form, �⃗�1 = 11.5N 𝑥 + 9.64N �̂� and �⃗�2 = −10N 𝑥, the net force

on the box can be determined with vector addition, �⃗�total = �⃗�1 + �⃗�2 = (11.5N �̂� + 9.64N �̂�) +

(−10N 𝑥) = 1.5N 𝑥 + 9.64N �̂�.

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.

Experiment Procedures:

In this experiment, you are expected to perform the following steps in order to determine an

unknown force.

1. Use hanging masses to set up 3 known forces on a force table, 𝐹1 = 1.2~1.5N at 34°, 𝐹2 = 0.7~1.1N at 144° and 𝐹3 = 1.5~1.9N at 203°.

2. Use trial-and-error method to experimentally determine the magnitude and direction of the 4th force 𝐹4 which balances the existing 3 forces.

3. On a piece of paper, use vector calculation to numerically determine the magnitude and direction of the 4th force to balance the existing 3 forces.

4. In Microsoft Excel, record your data and set up formulas to repeat calculation in step 3, and save your Excel sheet for the Data Analysis, which involves calculation of 10 sets of data. The Excel can save you a substantial amount of time.

5. Compare the experimental result to the numerical result.

Please refer to the following images for more instruction of equipment setup and optimization.

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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 fine tune the forces.

Please note that there are two sets of angle readings on the force table, the inner and outer. One may choose either set as long as one stays consistent.

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.

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Experimentation Grades (30 points):

Inform your instructor once you confidently finish all experiment procedures. Your instructor will

assign your experimentation grade using the chart below.

Item 0 points 6 points

Data organization All data are randomly scattered. All data are recorded and organized in Excel for easy reading and calculation.

Force components calculation

Force components are calculated by hand.

Force components are calculated using Excel.

Force 𝐹4 Force 𝐹4 is missing. The magnitude and direction of both the calculated and the experimentally determined 𝐹4 are recorded for comparison.

Significant figures The processed data are reported with incorrect significant digits.

All force components and the magnitude of 𝐹4 are recorded with the correct significant digits.

Units Units are missing for all quantities. Proper units are included for all physics quantities.