(10%) Problem 7: A uniform stationary ladder of length Land mass M leans against
ID: 1454080 • Letter: #
Question
(10%) Problem 7: A uniform stationary ladder of length Land mass M 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 Au. The ladder makes an angle 0 with respect to the floor. A painter of weight 1/2M stands on the ladder a distance d from its base. Otheexpertta.com A 25% Part (a Find an expression for the magnitude of the normal force Nexerted by the floor on the ladder. A 25% Part (b) Find an expression for the magnitude of the normal force Nw exerted by the wall on the ladder A 25% Part (c Find an expression for the largest value of d for which the ladder does not slip A 25% Part (d) What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 5.5 m long, the coefficient of friction is 51, the ladder is at an angle of 43' and the ladder has a mass of 85 kg.Explanation / Answer
a)
Normal force acting on the wall,
N = m*g + M*g
= (M/2)*g + M*g
= 3*M*g/2
b) Apply, Fnetx = 0
mue*N - Fw = 0
==> Fw = N*mue
= 3*M*g*mue/2
c)
Apply net torque about the bottom = 0
M*g*(L/2)*sin(90 - theta) + (M/2)*g*dmax*sin(90-theta) - F_w*L*sin(theta) = 0
M*g*(L/2)*cos(theta) + (M/2)*g*dmax*cos(theta) - (3*M*g*mue/2)*L*sin(theta) = 0
L*cos(theta) + dmax*cos(theta) - (3*mue)*L*sin(theta) = 0
dmax*cos(theta) = (3*mue)*L*sin(theta) - L*cos(theta)
dmax = (3*mue)*L*tan(theta) - L
d) dmax = (3*0.51)*5.5*tan(43) - 5.5
= 2.347 m
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