PHYS 2425 – Engineering Physics I

Vector Equilibrium

 

Leader: _____________________________  Recorder: ___________________________

Skeptic: _____________________________ Encourager: _________________________

 

Materials


Force Table

Level, 6 in

Mass Hanger, 0.49 N

Mass Set, Newton

Protractor

Ruler, 15 in


Introduction

      In this brief lab, we will conduct several experiments to examine vector equilibrium.  Equilibrium of vectors means simply that the sum of the vectors equals zero.  In the first experiment we will hang weights attached by a string to a central point, and determine the direction where the weights must be located so that the entire apparatus is in equilibrium.  In the second experiment, we will place two weights in known directions, and calculate the weight needed so that when a third weight is added in a specified direction, equilibrium results.

In this laboratory we will make use of a force table as shown in Figure 1.

 

Figure 1  Force Table

The force table allows us to measure the direction of a force applied to the center ring, by reading the angle from the scale on the force table.  In this experiment we will use the force table to determine if the sum of several forces results in equilibrium, i.e. the force vectors add up to zero.  In the second part of the experiment we will find the angles such that three forces equal in magnitude add up to zero, and in the third part we will find the magnitude and direction of a third force such that it equilibrates the sum of two specified forces.

Procedure 1

For the first experiment, first make sure that the force table is level, and then suspend two mass hangers from the strings each with 2 N on them.  Make sure that the strings drape over two of the pulleys.

Q1)  Including the mass hanger which has a weight of .49 N, what is the weight in newtons due to each of the sets of weights?

 

 

Fix one of the pulleys at the 0° mark, and move the other pulley until equilibrium is achieved.  When the forces are not in equilibrium, the ring in the center will accelerate in the direction of the net force until caught by the pole in the center of the table.  When the forces are in equilibrium, the ring will remain in the center and not push up against the pole, as its acceleration is zero.

 

Q2)  When the force vectors are in equilibrium, how do the angles of the two pulleys compare?


Q3)  Is this what you would expect, based on the fact that the magnitude of each force vector is the same?  Explain.


No experiment is perfect.  Add the smallest weight in the set to one of the hangers.

Q4)  Does equilibrium still appear to result?  If so, suggest a reason for this possible error.  Your reason should be based on the behavior of the apparatus, and should include meaningless collectives such as “human error” or “experimental error”.


Remove the weight you just added and change the angle of one of the pulleys by 1°.

Q5)  Does equilibrium still appear to result?  If so, suggest a reason for the possible error.


Now add an additional .5 N to one of the mass hangers.

Q6)  Is it possible to find a position that will equilibrate the other vector?  Explain.


Q7)  Based on your observations here, explain the conditions that must be met in order for two forces to add resulting in equilibrium.

 

 

 

Q8)  In the space below show the vector sum of the two indicated vectors.   Label the sum C



Q9)  Compared to C, what vector must you add to A + B to obtain a vector sum of 0?

 

 

Procedure 2

For the second experiment, we will fix two force vectors, and calculate the magnitude and direction of the third force vector so that it will equilibrate the other two.  Hang weights on two mass hangers so that the total weights (including the hanger) are .99 N and 1.49 N from directions 0° and 150°, respectively.

 

Q10)  Calculate the force vector required to equilibrate the sum of the other two force vectors.  Express your answer in i) point form, ii) using unit vectors, and iii) giving magnitude and direction.  Show your work in the space provided below or on the back of this page.

 

 

Q11)  Verify that you are correct by placing this weight on the hanger, and orienting the pulley at the angle you determined and observe if equilibrium results.  If not, check your calculations and try again.  Once you are satisfied, show your work to your instructor.

 

Instructor’s Initials ___________

 

Q12)  Set up a coordinate system for your table with the origin in the center, the positive x-axis pointing towards the 0° mark, and the positive y-axis pointing towards the 90° mark.  Using this coordinate system, accurately sketch a graph of the three force vectors below.  Use a ruler and protractor to graph these vectors accurately, and show graphically that the sum of these vectors is zero.