Self-closing refrigerator door A door is constructed of a thin homogeneous slab of material of width w, with frictionless hinges. If the door is opened through an initial angle ao < π/2, and it is released at rest, it closes itself in a time t. Find a formula for the angle d that the line of hinges makes with the vertical, in terms of w, ao, t and g. Use your formula to find 8 (in degrees) for the case w=0.86m, ao = π/4, t = 1.5s, g = 9.81m/s². Is this consistent with your experience with your refrigerator? (Recall that the moment of inertia of a rod of mass m and length & about one of its ends is ml²/3.)

Self-closing refrigerator door A door is constructed of a thin homogeneous slab of material of width w, with frictionless hinges. If the door is opened through an initial angle ao < π/2, and it is released at rest, it closes itself in a time t. Find a formula for the angle d that the line of hinges makes with the vertical, in terms of w, ao, t and g. Use your formula to find 8 (in degrees) for the case w=0.86m, ao = π/4, t = 1.5s, g = 9.81m/s². Is this consistent with your experience with your refrigerator? (Recall that the moment of inertia of a rod of mass m and length & about one of its ends is ml²/3.)

Elements Of Electromagnetics

7th Edition

ISBN:9780190698614

Author:Sadiku, Matthew N. O.

Publisher:Sadiku, Matthew N. O.

ChapterMA: Math Assessment

Section: Chapter Questions

Problem 1.1MA

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Concept explainers

Forming and Shaping

Metal forming is a category of metalworking process through which the material can be given the desired shape and size by subjecting it to plastic deformation, where the component undergoes bulk deformation process upon application of loads. Unlike the shearing and machining process, the material does not undergo up to a failure point as indicated in the stress-strain curve. Hence, the stresses induced during the forming process are greater than yield strength but less than the failure strength of the material. The process does not lead to the loss of material, so it can be said to be an economical process. During forming, the material is subjected to tensile forces, compressive forces, bending, and shearing loading conditions. The material should possess the property of ductility to undergo the forming process.

Question

Question 3. Please attempt.

(1) Make a
3. Self-closing refrigerator door A door is constructed of a thin homogeneous slab of material of width w, with frictionless
hinges. If the door is opened through an initial angle ao </2, and it is released at rest, it closes itself in a time t.
Find a formula for the angle & that the line of hinges makes with the vertical, in terms of w, ao, t and g. Use your
formula to find 8 (in degrees) for the case w = 0.86m, ao = π/4, t = 1.5s, g = 9.81m/s². Is this consistent with your
experience with your refrigerator? (Recall that the moment of inertia of a rod of mass m and length & about one of
its ends is ml2/3.)
Some possibly useful formulas:
F = ma,
p = mv, F = P₁
L=rxp, N = 7x F = L
W₁+2 = ₁² ds. F(F),.
Fk=kFN, 0 ≤ Fs ≤s FN,
F21 = -Gm₁m₂2₁-23, F21 = Q1Q2 71-773
1/μ = 1/m₁ + 1/m2, M = m₁ + m2, R= (miri+m₂r2)/M,
P = MR, T = MR² +47²2, L=Rx MR+Fx μr,
V(r) = ar+1 ⇒T="¹
T = T2 - T1
Central Potential Problem: Vor(r) = ² +V(r).
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