After the ice storm, a worker for the power company has to use a 10m-ladder (bec
ID: 2075543 • Letter: A
Question
After the ice storm, a worker for the power company has to use a 10m-ladder (because they ran out of trucks) to reach the top of an icy (very slippery) 9.0 m-power pole to assess damage. The 90 kg-worker chips the ice off the ground increasing the coefficient of friction to 0.45 between the ladder and the ground. The worker places the 30 kg-ladder at an angle theta = 64.2 degree with respect to the ground and starts climbing the ladder. (Situation in the figure to the right.) Draw the extended freebody diagram for the ladder. For right now, just assume a position for the worker on the ladder (indicate it on your figure). Determine the magnitude of the normal force by the ground on the ladder. Determine the magnitude of the force of static friction by the ground on the ladder. Determine the magnitude of the contact force by the pole on the ladder. Determine how high up the ladder the worker can go without the ladder slipping.Explanation / Answer
Forces acting in the given setup:
Weight mg of the man acting vertically downwards from a distance x from the point of contact of ground and ladder.
Weight Mg of the ladder acting vertically downwards from the center of the ladder.
Vertical normal force S acting upwards from the point of contact of ground and ladder.
Horizontal normal force R acting to left from the point of contact of wall and ladder.
Now, the net force in vertical and horizontal direction is zero. Therefore, we can write:
S - mg - Mg = 0
b] S = (90 + 30)9.8 = 1176 N
also, R - Fr = 0
=> R - (0.45)S = 0
=> R = (0.45)(1176) = 529.20 N
c] therefore, Fr = R = 529.20 N.
d] R = 529.20 N
e] Net torque on the ladder is zero. So, taking the torque about the point of contact of ground and ladder we get:
Mnet = - mgxcos64.2 - Mg(L/2)cos64.2 + RLsin64.2 = 0
=> - 90(9.8)xcos64.2 - 30(9.8)5cos64.2 + 529.20(10)sin64.2 = 0
=> x = 10.745 m which is greater than L = 10 m
therefore the worker can climb up the entire length of the ladder without the ladder slipping.