Question

A lightweight string of length 60.0 cm is attached to the ceiling at poins separated by distance d, as shown in the diagram below. Three objects of equal mass are hung from the sting. separatin the sttring into four equal segments of Legth L. If angle =40 degrees, find the measure of and and the distance d.

For full credit on problems:

1. Draw a picture and label the info, show direction of acceleration.

2. Choose objest for which to draw a free body diagram.

3. Draw free body diagram for each object, and define the x and y axes.

4. Split your forces into components.

5. Write out equations and then solve.

Answers are 15.6 degrees, and 51.9 cm... I just want to see how the work is done to get to these answers

5. write out the equations and then solve.

http://websites.rcc.edu/cheney/files/2014/08/Physics-2A-Homework-4.pdf

Use the link provided for the diagram, it is the last one on the sheet.

Answer 1

total length = 60 cm

length of each of 4 sections = L = 60 / 4 = 15 cm = 0.15 m

2 L Cos + 2 L Cos = d

2(0.15) (Cos + Cos ) = d

0.3 (Cos40 + Cos ) = d

0.23 + 0.3 Cos = d                    eq-1

force equation along the vertical direction is given as

T₁ Sin = mg + T₂ Sin                     eq-2

force equation along the horizontal direction is given as

T₁ Cos = T₂ Cos eq-3

for the weight in the middle . force equation in vertical direction is given as

T₂ Sin + T₂ Sin = mg

2T₂ Sin = mg                                

T₂ Sin = mg/2                               eq-4

Using eq-2 and eq-4

T₁ Sin = mg + mg/2 = 3mg/2

T₁ Sin = 1.5 mg             eq-5

dividing eq-5 by eq-3

tan = 1.5 mg / T₂ Cos

Cos = 1.5 mg / (T₂ tan )   

Cos = 1.5 mg 2 Sin/ (mgtan )

cot = 3/tan40

= 15.6

Using eq-1

0.23 + 0.3 Cos15.6 = d   

d = 0.5189 m = 51.89 cm