Question

The Department of Art and Art History is preparing an exhibit at the Art Gallery. They have asked the engineering program to help, and you have volunteered. A large sculpture needs to be mounted to the wall, and the curator is unsure if a ladder can be used or if she must rent a scissor lift. The ladder that the department has is 3.0 m long and has a mass of 20 kg. When propped up against the wall such that the sculpture can be installed, the ladder makes an angle of 45° with respect to the floor. You have determined that the coefficient of static friction is ?_s = 0.50 for the ladder-floor system. Assume the wall is frictionless. If you have a mass of 50 kg, and the sculpture has a mass of 10 kg, will the ladder be sufficient or will a scissor lift be needed to be rented?

Answer 1

W1= weight of ladder= 20*9.8

W2= weight of you + sculpture= 60*9.8

F2= ?s*N2= 0.5N2

From horizontal equilibrium, N1= F2= 0.5N2

From vertical equilibrium, W1+ W2= N2

So, N2= 784N and

F2= N1= 392N

Now, about point of contact of ladder with wall, net moment is 3cos(45)*N2 - 1.5cos(45)*W1 - 3cos(45)*F2 = 623.66 N-m , which is anticlockwise and tends to slip the ladder. So , the ladder won't be sufficient and a scissor lift will be needed to be rented.