A uniform stationary ladder of length L = 4.9 m and mass M = 11 kg leans against

Question

A uniform stationary ladder of length L = 4.9 m and mass M = 11 kg leans against a smooth vertical wall, while its bottom legs rest on a rough horizontal floor. The coefficient of static friction between floor and ladder is mu = 0.45. The ladder makes an angle Theta = 51 degree with respect to the floor. A painter of mass 8M stands on the ladder a distance d from its base. Find the magnitude of the normal force N, in newtons, exerted by the floor on the ladder. Find an expression for the magnitude of the normal force Njj- exeited by the wall on the ladder. What is the largest distance up the ladder dinax. in meters, that the painter can stand without the ladder slipping! dmax = The ladder does not slip when static friction balances the other forces in the horizontal direction. What other forces are acting horizontally? This will require a carefully constructed free body diagram. Only the force of static friction and the normal force due to the wall are acting m the horizontal direction.

Explanation / Answer

a)
N = m*g = (M+8M)* g = 9*M*g = 9*11*9.8 = 970.2 N

b)
Nw = frictional force
= miu*N
= 0.45*970.2
=436.59 N

c)
torque along any point should be 0
let consider the torque through the bottom point of ladder be 0

then torque due to mg must balance torque due to NW

Torque due to mg = mg* perpendicular distance
= 970.2 * perpendicular distance
= 970.2 * d*cos thetha
= 970.2 * d* cos 51
=610.6 * d

torque due to Nw= Nw* h
= Nw*L*cos thetha
= 436.59*4.9* cos 51
= 1346.3 Nm

balance them:
610.6 * d = 1346.3
d=2.2 m
Answer: 2.2 m

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