Can give a real world-example for the questions (8 & 9) below??? also solve Ques

Question

Can give a real world-example for the questions (8 & 9) below???

also solve Question 8 & 9

Equation #1: M = 2m cos (/2)

Equation #2: = 2 cos -1 (M/2m)

Svmmetric Case with Four Masses This is a theory exercise. No measurements are necessary, unless you wish to use the force table to confirm vour results. Consider a symmetric case with three equal masses m and one dissimilar mass M. Let equal the angle between the two outermost masses m. (This setup is like the one in the theory section above, but with an additional mass m along the symmetry axis). Find an equation similar to Eq. 1 which expresses the m condition for balanced forces in terms of M, m, and 0. Hint: Use what you know about equilibrium and the same method as described in the theory summary to derive Eq. 1 . 8. ht ht 9. Now what is the range of allowed M values? (Give your answer in terms of m, as was done in the theory section.)

Explanation / Answer

Assuming that all the masses are moving with same velocity as shown in the figure. along the directions shown in the figure

from momentum conservation

Mv = 2mvcos(theta/2) + mv

or

8. M = 2m*cos(theta/2) + m

9. (M - m) = 2m*cos(theta/2)

theta = 2*arcos[(M - m)/2m]

or cos(theta/2) = (M - m)/2m

nnow - 1 < cos(theta/2) < 1

so, condition 1

(M - m)/2m > = -1

M - m > = -2m

M + m > 0 ( this is always true)

condition 2

(M - m)/2m <= 1

M - m <= 2m

M <= 3m

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