can someone help me solving this question? Consider an arbitrary number (N+ 2) o

Question

can someone help me solving this question?

Consider an arbitrary number (N+ 2) of equal masses (m) configured as in the figure. The N = 3 case is drawn. Clearly Define the coordinates for the location of each mass in your answer. Write down the equations F = ma for each of the masses. Use a free body diagram, neglect friction and express the force in terms of the cable's tension T Write down the constrain on the acceleration of each mass, resulting from the cable being in-extendible. Use the equations above to find T. Use T to find the acceleration of each mass.

Explanation / Answer

Here are 5 masses

on first and last masses

F=T-mg

For other masses

F = 2T -mg

For first and last mass,upward a1=(T-mg)/m

For others,upward a2= (2T-mg)/m

Acceleration of rope joining second and third pully a3=2a2 - - a3=2a2 +a1

because of symmetry acceleration of rope joining third- fourth pully and fourth-fiftg pully will be equal and equal to -a3

Downward Acceleration of middle mass a3 = 2a2+a1

(mg -2T )/m= (4T-2mg )/m + (T-mg)/m

mg - 2T = 5T -3mg

7T = 4mg

T =4mg/7

acceleration of first and last mass = (4g/7 -g)

= -3g/7 upward

acceleration of second and fourth mass a2 = (2T/m.-g) =g/7

Acceleration of third mass a3= -2a2 -a1 =-2g/7 +3g/7 =g/7

Related Questions

Navigate

• Browse (All)
• Browse C
• Subjects

---

---

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