Imagine Romeo is attempting to sneak into Juliet\'s second story room. Lord Capu
ID: 1999424 • Letter: I
Question
Imagine Romeo is attempting to sneak into Juliet's second story room. Lord Capulet has coated the building wall with a material so slippery that is has no friction, and Romeo cannot scale the wall. So Romeo brings a ladder with mass m, length L, and uniform mass density. He places the ladder against the building wall so the base of the ladder makes an angle with the ground (which has coefficient of static friction Mu > 0 Treating Romeo as a point particle with mass M, show that the ladder will slip and Romeo will faceplant when he has climbed a fraction x of the length of the ladder given by x 2Mu_s(m + M) tan theta -m/2M If theta = tan^-1(2) =equalent 63^degree, show that the minimum Mu_s between the ground and the ladder for Romeo to reach Juliet's room depends on the masses as Mu_s > equl to m+2M /(m + M)Explanation / Answer
balancing forces in vertical,
Nf = mg + Mg
and f = us Nf =us (mg + Mg)
balancing forces in horizontal,
Nw = f = us (mg + Mg)
now balancing moment for max xL where system remains in equilibrium.
moment about floor point,
net moment = (L/2 * mgcos@) + (xL * Mgcos@) - (L * Nw * sin@) = 0
(mgcos@/2) + (xMgcos@) - (us(Mg + mg)sin@ )= 0
x = (us(M + m)sin@ - mcos@/2 ) / ( Mcos@)
x = (2u(m + M)tan@ - m ) / 2M