To solve this problem we will apply the concepts related to energy conservation. From this conservation we will find the magnitude of the amplitude. Later for the second part, we will need to find the period, from which it will be possible to obtain the speed of the body.
A) Conservation of Energy,
Here,
m = Mass
v = Velocity
k = Spring constant
A = Amplitude
Rearranging to find the Amplitude we have,
Replacing,
(B) For this part we will begin by applying the concept of Period, this in order to find the speed defined in the mass-spring systems.
The Period is defined as
Replacing,
Now the velocity is described as,
We have all the values, then replacing,
Answer:
Explanation:
Hello,
Let's get the data for this question before proceeding to solve the problems.
Mass of flywheel = 40kg
Speed of flywheel = 590rpm
Diameter = 75cm , radius = diameter/ 2 = 75 / 2 = 37.5cm.
Time = 30s = 0.5 min
During the power off, the flywheel made 230 complete revolutions.
∇θ = [(ω₂ + ω₁) / 2] × t
∇θ = [(590 + ω₂) / 2] × 0.5
But ∇θ = 230 revolutions
∇θ/t = (530 + ω₂) / 2
230 / 0.5 = (530 + ω₂) / 2
Solve for ω₂
460 = 295 + 0.5ω₂
ω₂ = 330rpm
a)
ω₂ = ω₁ + αt
but α = ?
α = (ω₂ - ω₁) / t
α = (330 - 590) / 0.5
α = -260 / 0.5
α = -520rev/min
b)
ω₂ = ω₁ + αt
0 = 590 +(-520)t
520t = 590
solve for t
t = 590 / 520
t = 1.13min
60 seconds = 1min
X seconds = 1.13min
x = (60 × 1.13) / 1
x = 68seconds
∇θ = [(ω₂ + ω₁) / 2] × t
∇θ = [(590 + 0) / 2] × 1.13
∇θ = 333.35 rev/min
Answer:
The efficiency is 0.33, or 33%.
Explanation:
From the thermodynamics equations, we know that the formula for the efficiency of a heat engine is:
Where η is the efficiency of the engine, Q_1 is the heat energy taken from the hot source and Q_2 is the heat energy given to the cold object. So, plugging the given values in the formula, we obtain:
This means that the efficiency of the heat engine is 0.33, or 33% (The efficiency of an engine is dimensionless).
The equation we use is mλ=dsinθ for intensity maximas. We are given at the first maximum (m=1), it occurs at 17.8 degrees. Thus we can solve for d by substituting known values into our equation.
(1) (632.8*10^-9m)=dsin(17.8) => d = 2.07*10^-6m
Next we want to find the angle at the second maximum (m=2) so we need to solve for θ.
(2) (632.8*10^-9m) = (2.07*10^-6m)sinθ
θ=37.69 degrees
Hopes this helps!
P.S. I hope this is right. If not sorry in advance.
Answer:
31302 Volts and 55/111 Amps (≈0.5)
Explanation:
Secondary voltage / 141 = 1110 / 5
Secondary voltage = (1110*141) / 5
Secondary voltage = 31302
Amperage = 110/ (31302/141) = 55/111
