Question

A 60 kg sofa 4m long is carried by James and Sarah. James is holding the sofa 0.2m from an end. Sarah is holding the sofa by the other end. A passing moron places a 40 kg box of books on the sofa 0.5m from the end Sarah is holding. How much weight is sarah holding now.

Answer 1

Weight of sofa, Ws = m*g = 60*9.8 = 588 N

Weight of books, Wb = m*g = 40*9.8 = 392 N

length of sofa = 4 m, So center of mass of sofa will be at 2 m

James is at 0.2 from an end, So he is 1.8 m from the center of mass of sofa

Sarah is at the other end, So Sarah is at 2.0 m from center of mass sofa

Books are placed at 0.5 m from the sarah's end, So books are at 1.5 m from the center of mass of Sofa

Books are placed at 0.5 m from the sarah's end, So books are at 1.8 + 1.5 = 3.3 m from James

Suppose weight holded by sarah is W1 and Weight holded by James is W2, then

Now Using torque Balance about the James holding point,

Net torque = 0

W1*r1 - Wb*r2 - Ws*r3 = 0

W1 = (Wb*r2 + Ws*r3)/r1

r2 = distance between James and books = 3.3 m

r3 = distance between James and center of mass of Sofa = 1.8 m

r1 = distance between James and Sarah = 4 - 0.2 = 3.8 m

So,

W1 = (392*3.3 + 588*1.8)/3.8 = 618.95 N = 620 N

Please Upvote.