Answer:
a) k
= 3.6 N/m ; b) 9.43 * 10¹²; c) 1.18 * 10¹¹; d) 75.08 N/m
Step-by-step explanation:
Length of iron bar = L = 2.7m;
side length of cross section = a = 0.07cm = 0.0007m;
x = 2.7 cm = 0.027m;
m = 100kg;
ρ = 7.87gm/cm³;
da = 2.28 * 10⁻¹⁰m;
a)
Fnet = F - mg
where Fnet = 0
So,
F = mg where F=kx
k = mg/x = 100*9.8/0.027
k = 3.6 N/m
b)
Nchain = Aw/Aa =a²/(da)²
= (o.ooo7)²/(2.28 * 10⁻¹⁰)²
= 9.43 * 10¹²
c)
Nbond = L/da = 2.7/2.28 * 10⁻¹⁰
= 1.18 * 10¹¹
d)
Spring stiffness of wire = ksi = (Nbondk)/Nchain
= [(1.18* 10¹¹)(6*10⁴)]/(9.43 * 10¹²)
= 75.08 N/m
Step-by-step explanation:
2x + 1 = 16
2x = 15 (subtract 1 on both sides)
x = 7.5 (divide 2 om both sides)
Since 7.5 is not an integer, (a) is No.
However 7.5 is rational, therefore (b) is Yes.
Answer:
See below.
Step-by-step explanation:
By definition the median of the triangle bisects the base of the isosceles triangle.
We need to prove that the 2 triangles formed by the median are congruent.
If the 2 triangles are ABD and ACD where BD is the median and < ABC is the angle from which BD is drawn.
BD = BD ( the common side)
AD = DC ( because BD is the median).
AB = AC ( because ABC is an isosceles triangle).
So Triangles ABD and ACD are congruent by SSS.
Therefore m < ABD = m < CBD, so BD is the bisector of < ABC.
To prove BD is also the altitude:
Triangles ABD and CBD are congruent as we have just proven. Therefore the
of measure of the base angle ABD = m < CBD . Also they are adjacent angles ( on the same line) so they add up to 180.
Therefore angles ABD and CBD are both right angles and BD is the altitude of triangle ABC.
Either one at any given time could be equal to zero. So
x + 2 = 0
x = - 2
x - 18 = 0
x = 18
I've enclosed a graph of this so you can see that the answers I've given are the ones expected.
