Answer:
The spring constant = 104.82 N/m
The angular velocity of the bar when θ = 32° is 1.70 rad/s
Explanation:
From the diagram attached below; we use the conservation of energy to determine the spring constant by using to formula:


Also;

Thus;

where;
= deflection in the spring
k = spring constant
b = remaining length in the rod
m = mass of the slender bar
g = acceleration due to gravity


Thus; the spring constant = 104.82 N/m
b
The angular velocity can be calculated by also using the conservation of energy;






Thus, the angular velocity of the bar when θ = 32° is 1.70 rad/s
Answer:
The work done to get you safely away from the test is 2.47 X 10⁴ J.
Explanation:
Given;
length of the rope, L = 70 ft
mass per unit length of the rope, μ = 2 lb/ft
your mass, W = 120 lbs
mass of the 70 ft rope = 2 lb/ft x 70 ft
= 140 lbs.
Total mass to be pulled to the helicopter, M = 120 lbs + 140 lbs
= 260 lbs
The work done is calculated from work-energy theorem as follows;
W = Mgh
where;
g is acceleration due gravity = 32.17 ft/s²
h is height the total mass is raised = length of the rope = 70 ft
W = 260 Lb x 32.17 ft/s² x 70 ft
W = 585494 lb.ft²/s²
1 lb.ft²/s² = 0.0421 J
W = 585494 lb.ft²/s² = 2.47 X 10⁴ J.
Therefore, the work done to get you safely away from the test is 2.47 X 10⁴ J.
The two most common units of electric energy is Watts or hertz.
Answer: The speed necessary for the electron to have this energy is 466462 m/s
Explanation:
Kinetic energy is the energy posessed by an object by virtue of its motion.

K.E= kinetic energy = 
m= mass of an electron = 
v= velocity of object = ?
Putting in the values in the equation:


The speed necessary for the electron to have this energy is 466462 m/s
Answer:
t< 75 nm
Explanation:
A soap bubble is a thin film where when the beam enters the film it has a 180º phase change due to the refractive index and the wavelength changes between
λ = λ₀ / n
In the case of constructive interference in the curve of the spherical film it is
2 nt = (m + ½) λ₀
Where t is the thickness of the film and n the refractive index that does not indicate that we use that of water n = 1.33, m is an integer. The thickness of the film for the first interference (m = 0) is
t = λ₀ / 4 n
A thickness less than this gives destructive interference.
Let's look for the thickness for the visible spectrum
Violet light λ₀ = 400 nm = 400 10⁻⁹ m
t₁ = 400 10⁻⁹ / 4 1.33
t₁ = 75.2 10-9 m
Red light λ₀ = 700 nm = 700 10⁻⁹ m
t₂ = 700 10⁻⁹ / 4 1.33
t₂ = 131.6 10⁻⁹ m
Therefore, for all wavelengths to have destructive interference, the thickness must be less than 75 10⁻⁹ m = 75 nm
b) a film like eta is very thin, it is achieved when gravity thins the pomp, but any movement or burst of air breaks it,