<span>For this example, the value presented would be considered a statistic. The value is a statistic as it represents a numerical measurement of a sample. If it were a parameter, it would need to represent a numerical measurement of a population.</span>
Answer:
The least uncertainty in the momentum component px is 1 × 10⁻²³ kg.m.s⁻¹.
Explanation:
According to Heisenberg's uncertainty principle, the uncertainty in the position of an electron (σx) and the uncertainty in its linear momentum (σpx) are complementary variables and are related through the following expression.
σx . σpx ≥ h/4π
where,
h is the Planck´s constant
If σx = 5 × 10⁻¹²m,
5 × 10⁻¹²m . σpx ≥ 6.63 × 10⁻³⁴ kg.m².s⁻¹/4π
σpx ≥ 1 × 10⁻²³ kg.m.s⁻¹
Answer:
a. 21.68 rad/s b. 30.78 m/s c. 897 rev/min² d. 1085 revolutions
Explanation:
a. Its angular speed in radians per second ω = angular speed in rev/min × 2π/60 = 207 rev/min × 2π/60 = 21.68 rad/s
b. The linear speed of a point on the flywheel is gotten from v = rω where r = radius of flywheel = 1.42 m
So, v = rω = 1.42 m × 21.68 rad/s = 30.78 m/s
c. Using α = (ω₁ - ω)/t where α = angular acceleration of flywheel, ω = initial angular speed of wheel in rev/min = 21.68 rad/s = 207 rev/min, ω₁ = final angular speed of wheel in rev/min = 1410 rev/min = 147.65 rad/s, t = time in minutes = 80.5/60 min = 1.342 min
α = (ω₁ - ω)/t
= (1410 - 207)/(80.5/60)
= 60(1410 - 207)/80.5
= 60(1203)80.5
= 896.65 rev/min² ≅ 897 rev/min²
d. Using θ = ωt + 1/2αt²
where θ = number of revolutions of flywheel. Substituting the values of the variables from above, ω = 207 rev/min, α = 896.65 rev/min² and t = 80.5/60 min = 1.342 min
θ = ωt + 1/2αt²
= 207 × 1.342 + 1/2 × 896.65 × 1.342²
= 277.725 + 807.417
= 1085.14 revolutions ≅ 1085 revolutions
Translating the first sentence into equation we get, t = k(1/h)
where t is time in seconds, k is the constant and h is the horsepower. Substituting
the values in the equation we have, 12s = k(1/200) we have a k = 2400 seconds –
hp. To get the time at 240 hp we use the equation above and the constant, we
get, t = (2400 seconds-hp)(1/240hp) t = 10seconds.
Explanation:
We have,
Length of a metal rod is 55 cm or 0.55 m
Change in length is 0.2 cm or 0.002 m
It is required to find the change in temperature of a metal rod. The coefficient of linear expansion is given by :
is the change in temperature
So, the change in temperature is 303.03 degrees Celsius.
