Answer:
29.4 N/m
0.1
Explanation:
a) From the restoring Force we know that :
F_r = —k*x
the gravitational force :
F_g=mg
Where:
F_r is the restoring force .
F_g is the gravitational force
g is the acceleration of gravity
k is the constant force
xi , x2 are the displacement made by the two masses.
Givens:
<em>m1 = 1.29 kg</em>
<em>m2 = 0.3 kg </em>
<em>x1 = -0.75 m </em>
<em>x2 = -0.2 m </em>
<em>g = 9.8 m/s^2 </em>
Plugging known information to get :
F_r =F_g
-k*x1 + k*x2=m1*g-m2*g
k=29.4 N/m
b) To get the unloaded length 1:
l=x1-(F_1/k)
Givens:
m1 = 1.95kg , x1 = —0.75m
Plugging known infromation to get :
l= x1 — (F_1/k)
= 0.1
Answer:
Explanation:
V = 100sin(ωt) + 150cos(ωt)
let x = ωt
V = 100sin(x) + 150cos(x)
a maximum or minimum will occur when the derivative is zero
V' = 100cos(x) - 150sin(x)
0 = 100cos(x) - 150sin(x)
100cos(x) = 150sin(x)
100/150 = sin(x)/cos(x)
0.6667 = tan(x)
x = 0.588 rad
V = 100sin(0.588) + 150cos(0.588)
V = 180.27756
as the maximum will not occur until ωt = 0.588 radians, for a cosine function we subtract that amount as a phase angle φ
V = 180.3 cos(ωt - 0.588)
or as a sine function, the phase angle lags the cosine by a difference of π/2
V = 180.3sin(ωt - (0.588 - π/2)
V = 180.3sin(ωt + 0.983)
Explanation:
One of the moments most valued by astronomers is twilight. As the Sun sets, the sky darkens and the first stars are seen. At first there are two or three, but as the minutes go by they become more and more visible; the first to appear will be the brightest stars of the night, the last, the dimmest. But their brightness is not the only thing that differentiates the stars. As the night progresses and the sky darkens, if we look closely, we will see stars of red, white and blue… Stars have colours, and learning about them takes us on a fascinating journey through their lives.
During these early spring weeks, it is easy to locate the constellation of Orion, along with Canis Major and Taurus, shortly after sunset. At first sight, the stars might appear to have the same colour, but if we seek out a dark sky and take a second closer look, we will notice different colours. Sirius (in Canis Major) is white, Rigel (Orion’s right foot) is blue, Aldebaran (in Taurus) is orange and Betelgeuse (Orion’s left shoulder) is red.
<span>Answer:
I guess there is is a typo in your question both change in enthalpy and change in internal energy for the combustion are negative:
â†H = -5074 kJ
â†U = - 5084.2 kJ
Work done to surrounding in a process is given by the integral:
W = â« P dV from initial to final volume
for a constant pressure process the integral simplifies to:
W = P â™ â« dV = Pâ™â†V
Enthalpy is defined as:
H = U + Pâ™V
So the change in enthalpy and the change in internal energy are related as:
â†H = â†U + â†(Pâ™V)
for a constant pressure process:
â†H = â†U + Pâ™â†V
Hence,
â†H = â†U + W
=>
W = â†H - â†U
= -5074 kJ - (-5084.2) kJ
= 10.2 kJ</span>
