Problem 3: A uniform stationary ladder of length L and 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 u. 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. Part (a) Find an expression for the magnitude of the normal force N exerted by the floor on the ladder. Expression : N = 3 Mg Select from the variables below to write your expression. Note that all variables may not be required. cos(a), cos(o), cos(0), cotan(0), sin(4), sin(0), tan(0), a, ß, u, n, 0, d, g, h, j, L, M, P, t Part (b) Find an expression for the magnitude of the normal force Nw exerted by the wall on the ladder. MultipleChoice : 1) Nw = Mg cot0 (1+d/2L) 2) Nw = 1/2Mg tan0 (1+d/L) 3) Nw 1/2Mg cot0 (1+d/L) 4) Nw = 1/2Mg cot0 (d/L) 5) Nw = Mg tan0 (1+d/L) Part (c) Find an expression for the largest value of dmax for which the ladder does not slip. Expression : dmax = L(3utan (o)-1) Select from the variables below to write your expression. Note that all variables may not be required. cos(a), cos(4), cos(0), cotan(0), sin(a), sin(4), sin(0), tan(8), a, u, T, g, L, M, t Part (d) What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 4.5 m long, the coefficient of friction is 0.54, the ladder is at an angle of 48.5°, and the ladder has a mass of 65 kg. Numeric A numeric value is expected and not an expression. dmax =
Problem 3: A uniform stationary ladder of length L and 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 u. 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. Part (a) Find an expression for the magnitude of the normal force N exerted by the floor on the ladder. Expression : N = 3 Mg Select from the variables below to write your expression. Note that all variables may not be required. cos(a), cos(o), cos(0), cotan(0), sin(4), sin(0), tan(0), a, ß, u, n, 0, d, g, h, j, L, M, P, t Part (b) Find an expression for the magnitude of the normal force Nw exerted by the wall on the ladder. MultipleChoice : 1) Nw = Mg cot0 (1+d/2L) 2) Nw = 1/2Mg tan0 (1+d/L) 3) Nw 1/2Mg cot0 (1+d/L) 4) Nw = 1/2Mg cot0 (d/L) 5) Nw = Mg tan0 (1+d/L) Part (c) Find an expression for the largest value of dmax for which the ladder does not slip. Expression : dmax = L(3utan (o)-1) Select from the variables below to write your expression. Note that all variables may not be required. cos(a), cos(4), cos(0), cotan(0), sin(a), sin(4), sin(0), tan(8), a, u, T, g, L, M, t Part (d) What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 4.5 m long, the coefficient of friction is 0.54, the ladder is at an angle of 48.5°, and the ladder has a mass of 65 kg. Numeric A numeric value is expected and not an expression. dmax =
College Physics
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Chapter1: Units, Trigonometry. And Vectors
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Please answer part d of question 3
Transcribed Image Text:Problem 3: A uniform stationary ladder of length L and 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 u. 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.
L
Part (a) Find an expression for the magnitude of the normal force N exerted by the floor on the ladder.
Expression :
N =
3 Mg
Select from the variables below to write your expression. Note that all variables may not be required.
cos(a), cos(), cos(0), cotan(0), sin(4), sin(0), tan(0), a, B, µ, T, 0, d, g, h, j, L, M, P, t
Part (b) Find an expression for the magnitude of the normal force Nw exerted by the wall on the ladder.
MultipleChoice:
1) Nw = Mg cot0 (1+d/2L)
2) Nw = 1/2Mg tan0 (1+d/L)
3) Nw= 1/2Mg cot0 (1+d/L)
4) Nw
5) Nw = Mg tan0 (1+d/L)
%3D
%3D
1/2Mg cot0 (d/L)
Part (c) Find an expression for the largest value of dmar for which the ladder does not slip.
Expression :
dmax =
L(3utan(0)-1)
Select from the variables below to write your expression. Note that all variables may not be required.
cos(a), cos(), cos(0), cotan(0), sin(a.), sin(o), sin(0), tan(0), a, µ, n, g, L, M, t
Part (d) What is the largest value for d, in centimeters, such that the ladder will not slip? Assume that ladder is 4.5 m long, the coefficient of
friction is 0.54, the ladder is at an angle of 48.5°, and the ladder has a mass of 65 kg.
Numeric : A numeric value is expected and not an expression.
dmax
%D
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