Answer:
the correct one is D
Explanation:
A question that can be answered with a scientific investigation must be a question where measurements of some kind can be made and with these measurements check that the question is correct or not.
When examining the answers the correct one is D
Answer:
Elevation =31.85[m]
Explanation:
We can solve this problem by using the principle of energy conservation. This consists of transforming kinetic energy into potential energy or vice versa. For this specific case is the transformation of kinetic energy to potential energy.
We need to first identify all the input data, and establish a condition or a point where the potential energy is zero.
The point where the ball is thrown shall be taken as a reference point of potential energy.
![E_{p} = E_{k} \\where:\\E_{p}= potential energy [J]\\ E_{k}= kinetic energy [J]](https://tex.z-dn.net/?f=E_%7Bp%7D%20%3D%20E_%7Bk%7D%20%5C%5Cwhere%3A%5C%5CE_%7Bp%7D%3D%20potential%20energy%20%5BJ%5D%5C%5C%20E_%7Bk%7D%3D%20kinetic%20energy%20%5BJ%5D)
m = mass of the ball = 300 [gr] = 0.3 [kg]
v = initial velocity = 25 [m/s]
![E_{k}=\frac{1}{2} * m* v^{2} \\E_{k}= \frac{1}{2} * 0.3* (25)^{2} \\E_{k}= 93.75 [J]](https://tex.z-dn.net/?f=E_%7Bk%7D%3D%5Cfrac%7B1%7D%7B2%7D%20%20%2A%20m%2A%20v%5E%7B2%7D%20%5C%5CE_%7Bk%7D%3D%20%5Cfrac%7B1%7D%7B2%7D%20%2A%200.3%2A%20%2825%29%5E%7B2%7D%20%5C%5CE_%7Bk%7D%3D%2093.75%20%5BJ%5D)
![93.75=m*g*h\\where:\\g = gravity = 9.81 [m/s^2]\\h = elevation [m]\\replacing\\h=\frac{E_{k}}{m*g} \\h=\frac{93.75}{.3*9.81} \\h=31.85[m]](https://tex.z-dn.net/?f=93.75%3Dm%2Ag%2Ah%5C%5Cwhere%3A%5C%5Cg%20%3D%20gravity%20%3D%209.81%20%5Bm%2Fs%5E2%5D%5C%5Ch%20%3D%20elevation%20%5Bm%5D%5C%5Creplacing%5C%5Ch%3D%5Cfrac%7BE_%7Bk%7D%7D%7Bm%2Ag%7D%20%5C%5Ch%3D%5Cfrac%7B93.75%7D%7B.3%2A9.81%7D%20%5C%5Ch%3D31.85%5Bm%5D)
Answer:
Ng = 0.893 N, Ne = 0.107N
Explanation:
Number of particles in Ground state = Ng
Number of particles in Excited state = Ne
Ne/Ng = e^{(-ΔE)/kt}
Since excited state is 3 fold degenerate
Ne/Ng =3 x e^{(-ΔE)/kt}
ΔE = Energy difference between ground and excited states = 0.25eV
T = 960 K
Constant k = 8.617 x 10^-5 eV/K
Ne/Ng = 3 x e^{-0.25/(8.617x10^-5) x 960}
= 3 x e^(-3.188645)
= 3 x 0.0412 = 0.1237 ≅ 0.12
Ne = 0.12 Ng
but Ne + Ng = N, where is N is total number of particles, substituting Ne into equation we get,
Ng(1 + 0.12) = N
Ng = N/1.12 = 0.893N
and Ne = 0.12 x 0.893 N = 0.107 N
Answer:
a. 0.143 mm b. 77.6 rad/m c. 483.18 rad/s d. +1
Explanation:
a. ym
Since the amplitude is 0.143 mm, ym = amplitude = 0.143 mm
b. k
We know k = wave number = 2π/λ where λ = wavelength.
Also, λ = v/f where v = speed of wave in string = √(T/μ) where T = tension in string = 19.3 N and μ = mass per unit length = 5.12 g/cm = 5.12 ÷ 1000 kg/(1 ÷ 100 m) = 0.512 kg/m and f = frequency = 76.9 Hz.
So, λ = v/f = √(T/μ)/f
substituting the values of the variables into the equation, we have
λ = √(T/μ)/f
= √(19.6 N/0.512 kg/m)/76.9 Hz
= √(38.28 Nkg/m)/76.9 Hz
= 6.187 m/s ÷ 76.9 Hz
= 0.081 m
= 81 mm
So, k = 2π/λ
= 2π/0.081 m
= 77.6 rad/m
c. ω
ω = angular frequency = 2πf where f = frequency of wave = 76.9 Hz
So, ω = 2πf
= 2π × 76.9 Hz
= 483.18 rad/s
d. The correct choice of sign in front of ω?
Since the wave is travelling in the negative x - direction, the sign in front of ω is positive. That is +1.
