Carol tries to push a bookshelf across the room. As much as she tries, she can not get the bookshelf to move. Which statement be
1 answer:
You might be interested in
Answer:
1) f= 8.6 GHz
2) t= 0.2 ms
Explanation:
1)
- Since microwaves are electromagnetic waves, they move at the same speed as the light in vacuum, i.e. 3*10⁸ m/s.
- There exists a fixed relationship between the frequency (f) , the wavelength (λ) and the propagation speed in any wave, as follows:
- Replacing by the givens, and solving for f, we get:
⇒ f = 8.6 Ghz (with two significative figures)
2)
- Assuming that the microwaves travel at a constant speed in a straight line (behaving like rays) , we can apply the definition of average velocity, as follows:
where v= c= speed of light in vacuum = 3*10⁸ m/s
d= distance between mountaintops = 52 km = 52*10³ m
- Solving for t, we get:
⇒ t = 0.2 ms (with two significative figures)
Answer:
a) the maximum shear stress τ the bar is 16T
/πd³
b) the angle of twist between the ends of the bar is 16tL² / πGd⁴
Explanation:
Given the data in the question, as illustrated in the image below;
d is the diameter of the prismatic bar of length AB
t is the intensity of distributed torque
(a) Determine the maximum shear stress tmax in the bar
Maximum Applied torque T_max = tL
we know that;
shear stress τ = 16T/πd³
where d is the diameter
so
τ = 16T
/πd³
Therefore, the maximum shear stress τ the bar is 16T
/πd³
(b) Determine the angle of twist between the ends of the bar.
let theta () be the angle of twist
polar moment of inertia = πd⁴/32
now from the second image;
lets length dx which is at distance of "x" from "B"
Torque distance x
T(x) = tx
Elemental angle twist = d = T(x)dx / G
so
d = tx.dx / G(πd⁴/32)
d = 32tx.dx / πGd⁴
so total angle of twist will be;
=
=
32tx.dx / πGd⁴
= 32t / πGd⁴
= 32t / πGd⁴ [ L²/2]
= 16tL² / πGd⁴
Therefore, the angle of twist between the ends of the bar is 16tL² / πGd⁴
