Question

Hello there,

I have this question due tomorrow, and every time I am trying to solve it, I am getting the wrong answer, any help as soon as possible would be appreciated,

Thank you very much.

Problem 2. Static Equilibrium. A 10kg, 2m long plank rests against a wall at one end and is held up by a SPRING connected at the other end. An additional mass of 5kg is hung from the plank at 0.8m from the wall. If that spring is extended 10 cm beyond its equilibrium length, what is the spring constant of the spring? What is the minimum coefficient of static friction between the plank and the wall? SPRING 0.8 m m 5 kg

Answer 1

spring force = kx

now torque about the contact point of wall and plank should be balanced

=> k*0.10*sin(30 degrees)*2 = 5*9.8*0.8 + 10*9.8*1

=> spring constant , k = 1372 N/m

friction force , f = Us*N = Us*(kx*cos(30 degrees))

equillibrium equation

f + kx*sin(30 degrees) = 5g + 10*g

=> f = 15*9.8 - 1372*0.10*0.5 = 78.4

=> 78.4 = Us*1372*0.1*0.866

=> friction coefficient , Us = 0.659