FIRST QTR LAB - L4 - TITLE: CONCURRENT VECTORS – The Law of Equilibrium
READING TO DO: TEXT: p92-97.
All lab reports must start with your name and physics class section. Next the TITLE
of the lab, and then the 7 SECTIONS BELOW. Please staple your report.
WHAT TO DO: #1- PURPOSE OF LAB (Clearly state all parts.)
“To attempt to prove the law of equilibrium for three concurrent forces acting on a
ring (and to obtain a percent discrepancy for forces in both the X & Y directions)”
HOW TO DO IT: #2- METHOD & MATERIALS (& ANY DIAGRAMS)
(List all materials and describe all procedures performed in your own words.)
a)Avoid the case of three 120 degree angles, or where one angle is too small.
b)For best results, all three spring scales should read between 10 and 17 newtons.
c)Construct a neat vector diagram; use a protractor to accurately measure <q1 & <q2.
d)With pencil, ruler, & protractor, redo and enlarge this diagram, using a scale so
that vector lengths represent their actual values in newtons; label diagram fully.
WHAT TO MEASURE; WHAT DATA TO COLLECT:
#3- DATA CHARTS (Properly labeled, with all measurement units)
a)Set F3 pointing West on the X-axis, and follow the directions in the DIAGRAM and
CALCULATIONS(etc) sections that follow on the next page.
b)Carefully record the readings for F1, F2, & F3 in newtons & the values of <q1 & <q2.
WHAT & HOW TO CALCULATE OR PLOT:
#4- EQUATIONS & CALCULATIONS (Shown neatly & well organized)
EQUATIONS: The sum of all X Forces must = 0, AND the sum of all Y Forces must = 0.
Use the sine and cosine of the two measured angles q1 & q2 to find the four components.
Find X and Y components of F1 & F2, & along with F3, test the above law mathematically.
WHAT RESULTS TO LIST & EVALUATE:
#5- CHART OF RESULTS (Neatly arranged; Include units.)
The X and Y components of F1 & F2, the sum of the forces for both the X and Y
directions, and two % discrepancy results, one for the X and one for the Y forces.
(In % discrepancy formula denominators should be an average of the two values compared)
#6- DISCUSSION OF RESULTS & CONCLUSIONS:
Discuss your results, their accuracy, and the lab experiment in general. You may include anything relevant to the lab, like applications of major laws and concepts in the experiment. Evaluate whether you've achieved all the parts of the purpose of the lab, explain any problems encountered, and draw your final conclusions regarding the
purpose of the experiment.
P2 LAB NUMBER: L4
#7- WHAT QUESTIONS TO ANSWER: (on the last page of the lab report)
Define in complete sentences: Concurrent, component, equilibrant, law of equilibrium.
BACKGROUND INFORMATION:
1)An object is in translational EQUILIBRIUM when it is at rest, OR moving in a straight
line at a constant speed. Two other types of equilibrium that can exist are
rotational and vibrational equilibrium.
2)THE LAW OF EQUILIBRIUM is a corollary of Newton's first law of motion. It states:
"When an object is in translational equilibrium, the vector sum of all forces acting
upon it must equal zero." This means that all forces acting on the object are
cancelled by other equal but opposite forces. Therefore, if the object is at rest,
it remains at rest, and if it is moving straight ahead at a constant speed, it will
continue to do so if it remains in equilibrium.
3)In this lab, the ring is in translational equilibrium when motionless, with the
three spring scales locked in any position.
4)Since all forces have horizontal(X) and vertical(Y) components that can be calculat-
ed, a further corollary is: "When an object is in translational equilibrium, the sum
of the X Forces acting on it must equal zero, AND the sum of the Y Forces acting on
it must equal zero."
DIAGRAMS: (Refer to the sketches shown on the boards in the lab.)
1)Redraw your vector diagram but now use a convenient scale to show each vector's
length. Be sure that one of the vectors is on a horizontal line on your paper, and
that it points left. Label it F3. Draw the X axis along this line that goes between
the other vectors. Label the top vector F1 & the bottom one F2. Label the angles
that form between the vectors & the X axis as theta 1(top angle) & theta 2(bottom).
2)Now draw perpendiculars from the tip of vectors F1 and F2 to the X axis. Draw the
X and Y components of both vectors which appear in the triangles that are formed.
Label them F1x & F1y, and F2x & F2y.
3)Redraw these two triangles separately, label them fully, and now use them to
calculate the X & Y components of F1 and F2. To do this, write an expression for
both the sine and cosine of theta 1 & theta 2. Then solve the resulting equations
for F1x, F1y, F2x, & F2y, all of which appear in numerators of one of the equations.
CALCULATIONS, RESULTS CHART, & DISCUSSION: (Show All work & units.)
1)From the diagram completed as described above, calculate the values of F1x, F1y, F2x,
& F2y in newtons.
2)Use the above values, F3, & your knowledge of vectors and equilibrium, to calculate
the sum of the X Forces acting on the ring; AND calculate the sum of the Y Forces
acting on the ring.
3)Does F1x and F2x added together equal about the value of F3? Do a percent
discrepancy between left(F3) and right(F1x + F2x) forces.
4)Are the values of F1y and F2y about equal to eachother? Do a percent discrepancy
between up(F1y) and down(F2y) forces.
5)Make a chart of results listing F3 vs (F1x + F2x), and F1y vs F2y, along with the
percent errors you obtained for each axis or direction.
Also list your results for the sum of the X Forces & the sum of the Y Forces acting
on the ring when it was in equilibrium.