Translational Equilibrium. We would like to introduce a concept called the polyg

Question

Translational Equilibrium.

We would like to introduce a concept called the polygon of forces, first used by Squire Whipple, an American engineer who develop the technique of analyzing a truss and put his ideas into a foundational 1847 book on bridge building.

See problems in an attachment.

90 0.50 N 1.00 N 180 2.00 270 Fig. 2: Example of how to sketch the force vectors in the grid Procedure 1. In each of the following situations, start with 100 g hanging from the 0° mark. For ease of 2. Experimentally determine the mass(es) and/or location(s) required to restore static 3. After you establish static equilibrium, record the mass(es) and the corresponding force(s) for calculation, you may use g=10m/sec" in all part of this lab equilibrium that mass as well as the location(s) 4. Below each situation is an overhead view of the force table. Carefully sketch all the forces acting on the ring for that situation by drawing the force vectors for each hanging mass by using the following scale: an arrow 1.0 cm long correspond to a 0.5 N force. (Then if you have 1.0 N pulling along the 0° line, you would draw an arrow 2.0 cm long pointing to the right as shown here: ) 5. Use the ruler to accurately measure the proper length for each vector and the protractor to accurately sketch the direction of the each force Note: In the Homework Questions, you will be asked to graphically "add" the force vectors for each scenario in a "head-to-tail" fashion. In order to make interpretation of your results easier, the vectors you sketch need to accurately reflect the relative magnitudes and direction of the forces acting on the ring. Be sure to use a protractor and straightedge when making your sketches.

Explanation / Answer

2. for all the 5 situations, the resultant force after all the individual forces have been added is 0, because all the forces are a part of a closed polygon. Hence

it is consistent with the observation of a ring that remained in static equilibrium, as for net force to be 0, the ring has to be under static equilibrium.

Activity 1.1

here assume that we are using 4 masses

so let the masses be m1 = 2 g

m2 = 5g

m3 = m g

m4 = 1 g

now, lets also assume that we have kept mass m1 at theta = 0 deg

m2 at theta = 90 deg

m4 at theta = 180 deg

so we can find a location for m3 so that the system remains in static equilibrium

let this angle with the 0 deg mark be phi in counterclockwise direction

hence

for analytical calculation consder i and j to be unit vectors

so from the condition of static equilibrium from newtons' second law

m1*g - m4*g + m3*cos(theta) = 0

m2*g + m3*gsin(theta) = 0

mcos(theta) = 1 - 2 = -1

msin(theta) = -5

m^2 = 1 + 25 = 26

m = 5.099019g

theta = 258.69 deg

hence by knowing the location and value of the three masses we can find the value of a fourth mass which can be uised to make the resultant of the force on the ring to be zero at some angle

Related Questions

Navigate

• Browse (All)
• Browse T
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.