What Is A Force Table

Physics 203 - Lab two - Vectors

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Introduction

Force Tables

The Force Table allows us to manipulate and measure out the effects of vector quantities.

Goals

The object of this lab is to proceeds a thorough understanding of vector improver. This is accomplished by using the strength tables to constitute equilibrium for a particle, and correlate this equilibrium condition with the math of vector add-on. Two methods of vector improver are discussed: graphical and belittling.

Equipment bank check

Please make sure your station has all of the following items. If non, check again, then talk to your lab instructor.

Intro to Vectors

Physical quantities that crave both a magnitude and direction for their description are vector quantities. A slap-up case of a vector quantity is the wind velocity. Since the current of air can blow in a direction, and with a certain speed, nosotros will demand to utilize both a magnitude and a direction to describe this concrete quantity.

Interactive Task

On the map of New York below, manipulate the wind vector (by dragging the tip of the arrow) until you go a wind speed of ten mph pointing in exactly the N East direction.

Task has been completed

Calculation Vectors

Vectors must exist added by special rules that take both parts of the description into account.

Below are two blue vectors, and the vector sum, a dashed black line. Attempt manipulating the blueish vectors and observing what happens to the sum.

Nigh the Force Table

Allow's empathize exactly how the force table works. A mass is placed in each pan (each pan has a mass of 50g). This mass experiences a force due to gravity given by its mass times $g$ . This strength is acting in the vertical management. In gild to redirect the force to human activity in a horizontal direction (i.e parallel to the surface of the table), chords and pulleys are used. Thus, the tensions from the chords on the ring at the middle are equal in magnitude to the force due to gravity on the pan + mass: $$T_1 = m_1 g$$ Attaching several pan/pulley systems to the table allows the states to pull on the ring with different tensions in different directions.

What will the tension be, in Newtons, if a 20 gram mass is attached to the 50g tray?

Tension [Due north] = delight log in

Instructions for use:

The cardinal ring has spokes that connect the inner and outer edges. When connecting the cords be certain that the hooks have not snagged on a spoke. In that case the cord volition not be radial. Too whenever you modify a caster position, check that the cord is however radial.
Be sure that when you position a pulley, that both edges of the clamp arc snugly against the edge of the strength table. Check that the string is on the pulley.
At that place are 2 tests for equilibrium.
1. The starting time test is to move the pin upward and down and observe the band. If information technology moves with the pin, the system is NOT in equilibrium and forces need to be adjusted.
2. The second test is to remove the pin. Nevertheless, this should be washed in 2 stages. First just lift information technology but hold it in the band to prevent large motions. If there is no movement, remove it completely. If the ring remains centered and so the organization is in equilibrium.

Exp. 1: Sensitivity of the musical instrument

Let's mensurate how precise the force tables are.

Adjust 2 pulley systems, Pan 1 at 0° and Pan two at 180°.
In Pan 1, place l grams. In Pan two, also place 50 grams.
At present, in Pan 2 add ane gram and cheque for equilibrium. Information technology's most probable nonetheless in equilibrium, right?
Find the maximum mass you lot can identify in pan 2 and however maintain experimental equilibrium.

Tape this value below. This is the sensitivity to weight of the force tabular array.

Sensitivity [g] = please log in

What factors could contribute to this sensitivity?

Resultant Vs. Equilibrant

A bespeak to exist aware of is that the force needed to balance the system is not the resultant of the weights, but the negative of that vector, also called the equilibrant. force table equilibrant

Response:

If the resultant of two mass/tray systems points in a management 234° measured counter-clock-wise (CCW) from the 0° line, in what direction should the equilibrant point?

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Experiment 2: Symmetric System

Using the number generator below, pick two initial masses and directions. Write these down in your notebook!

Mass 1: x grams

Direction ane: x °

Mass 2: x grams

Management 2: 10 °

Prepare two pans and mass systems based on these values.
Experimentally residual the system. (i.due east. without performing any math or belittling operations, find a third pan/mass system that will remainder the outset two.)

Mass needed to balance the Organisation [g] = please log in

Use the fake force table below to predict how much mass you should need and compare this to the value you institute experimentally. Make sure to include the mass of the pans in when setting up the forces. (You can employ $g \approx 10 m/southward^two$ for this)

Past how many grams was your experiment different from this simulation?

Grams divergence = please log in

Report the deviation between what you've experimentally measured and what the simulation predicted. Are they within the expected sensitivity of the instrument?

Vector Components

Our mathematical framework for dealing with multiple vectors involves using vector components. If we have an x-y coordinate centrality, any vector on this axis tin be decomposed into its x and y components. The simulation beneath shows one vector decomposed into its x and y components.

Question: Components

On the simulation above, pick a magnitude and direction for the dark royal vector. Pick a direction that points in both ten and y, i.east. not vertical or horizontal. Using trigonometry, calculate the magnitudes and direction of the vector components. Verify that your calculations match the predicted values of the components in the simulation. (Hovering the mouse overt the arrow tip will brandish its magnitude and management)

We'll need vector components to do more complicated calculations every bit the next department shows.

Experiment 3: Vector Components

This experiment volition demonstrate the concept of vector components.

With the pin in the strength table (i.e. and then the band doesn't move), hang one fifty gram mass from a pan at an bending of 35 degrees (CCW from the 0° line). This will create a forcefulness acting on the ring. We can call information technology $F_1$.
The adjacent step is to analytically calculate the x and y components of this strength. In other words, observe $F_{1x}$ and $F_{1y}$. Enter the magnitudes of these components in the boxes below.

$F_{1x}$ = delight log in

$F_{1y}$ = please log in

Now that y'all know what the 10 and y component magnitudes are of force $F_1$, you tin hang masses at 180 ° and 270 ° to rest each of the components of $F_1$ based on the calculations. Practise it and ostend that the organization is in equilibrium by pulling out the pin.

Include the results and piece of work of this calculation in the lab report. Also, draw a graphical vector diagram that shows how the system should be in equilibrium.

Multiple Forces

Interactive Task

An airplane in flying will have many forces acting on it. In the most simplified model, nosotros can consider 4 major contributors: weight, lift, drag, and thrust. Your chore: Balance the forces on this plane then that aeroplane would wing with a compatible velocity. (i.e. $F_\textrm{cyberspace} = 0$.)

Task has been completed

Exp. 4: Return to the Force Table

Now let's apply these concepts to the force tabular array. If we have 3 known forces acting, we should exist able to analytically predict a quaternary strength to add and then that the system is in equilibrium, i.e. $F_\textrm{net} = 0$.

Printing the blue push beneath to generate 3 sets of random masses and directions

Vector $\overrightarrow{A}$

Mass ane: ten grams

Direction i: x °

Vector $\overrightarrow{B}$

Mass 2: 10 grams

Direction 2: x °

Vector $\overrightarrow{C}$

Mass 3: x grams

Management 3: x °

Now, use component algebra to summate a along vector, $\overrightarrow{D}$, that when added to the system will result in equilibrium

The Equation you are essentially trying to solve is: $\overrightarrow{A}+\overrightarrow{B}+\overrightarrow{C}+\overrightarrow{D}=0$

Once y'all have arrived an answer, enter the components of the vector in the boxes below

$|D_x| = $ = please log in

$|D_y| = $ = please log in

Employ trig to convert your answer back to a magnitude and degree format. Add all four mass/pan systems (3 from the above, the fourth from your prediction) to the table, and verify that the prediction does indeed residual the arrangement.

Give the details of this adding and compare your analytical results with the the experimental results.

Depict a vector diagram that shows the table arrangement.

Done?

First, cheque your station for the equipment. Please return the station to a corking and orderly arrangement as shown in this motion picture. Once you lot accept done that, click the checkbox below.

Now, click this button beneath to view your filled out worksheet. Print it out and get it signed by your lab instructor before leaving.

Worksheet