Question

The Department of Art and Art History is preparing an exhibit at the UNO 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?

Im asking for a physics diagram of the problem along with all the eqaution laid out before the variables are pluged in. Thank you

Answer 1

Let a ladder be inclined to a wall on the right side. The ladder is placed such that the angle between the ground and the ladder is 45 degrees

Weight mg of the ladder acts vertically downwards from length L/2 where L is the length of the ladder

Weight Mg of the person climbing along with the sculpture acts vertically downward from a distance x along the ladder.

Normal force R acts vertically upwards from the point of contact of ground and ladder.

Normal force S acts horizontally to the left from the point of contact of ladder and the wall

and lastly, friction force F acts horizontally to the right.

then, for equilibrium of the system, the net force in both horizontal and vertical direction should be zero and also the net torque on the system should be zero.

so,

R = (M + m)g = (10 + 50 + 20)g = 784 N

and S = F = u_rR

=> S = 0.5(784) = 392 N

and taking torque about the point of contact of ground and ladder gives,

=>

=> x = 1.5 m

so, the sculpture can only be raised up till half of ladder's length which is not sufficient. Therefore, a scissor lift will be needed.