Question

5. [1pt] Four identical books of mass 790 g and width a = 224 mm are stepped equally and so as to maximize the overhang, d. Calculate d. Answer: ( Submit All Answers Not yet correct, tries 4/15

Could you please help with question 5 and 1

NOTE: the answer for question 5 is NOT 112mm, 224mm, 37.33mm

NOTE: the answer for question 1 in NOT FTFTF, FTTTT, FTFTT, FTTTF

Answer 1

Q5)

let each book be stepped by x. Hence, d = 3x.

Free body diagram for fourth book from bottom is as shown:

mg N4

Hence,

N4 = mg _______ eq.1

Free body diagram for third book from bottom is as shown:

N4 х mg уз N3 b0

Vertical force balance gives:

N3 = mg + N4 = 2mg ______ eq.2

Torque balance about Centre of mass gives:

N4*x = N3*y3

or y3 = N4/N3*x = x/2 _______ eq.3

also y3 <= a/2 - x (for maintaining contact with the book below)

or

x <= a/3 _________ eq.4

Free body diagram of second book from bottom is as shown:

N3 mg N2 у2

Vertical force balance gives:

N2 = mg + N3 = 3mg _______ eq.5

torque balance about center of mass gives:

N2*y2 = N3*(x + y3)

or y2 = N3/N2*(x + x/2) = x _____ eq.6

also, y2 <= a/2 - x (for maintaining contact with the book below)

or

x <= a/4 __________ eq.7

free body diagram for the first book from bottom is as shown:

Е N2 х+ у2 mg N1 yl

Vertical force balance gives:

N1 = mg + N2 = 4mg _______ eq.8

torque balance about center of mass gives:

N1*y1 = N2*(x + y2)

or y1 = N2/N1*(x + x) = 3x/2 _____ eq.9

also,

y1 <=a/2

or

x <= a/3 __________ eq.10

from eq.10, eq.7 and eq.4, we may see that the largest possible value of x is a/4 (using eq.7)

hence, d (maximum) = 3*x = 3/4*a = 3/4*224 = 168mm _________________ Answer

NOTE: As per Chegg guidelines, I may only answer one question at a time. The other question is to be asked separately.