Answer:
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Explanation:
Given data
mass = 3 slugs = 3 * 32.14 = 96.52 lbs
constant k = 9 lbs/ft
Beta = 6lbs * s/ft
mass is pulled = 1 ft below
to find out
equation of motion for the mass
solution
we know that The mass is pulled 1 ft below so
we will apply here differential equation of free motion i.e
dx²/dt² + 2 α dx/dt + ω² x =0 ........................1
here 2 α = Beta / mass
so 2 α = 6 / 96.52
α = 0.031
α² = 0.000961 ...............2
and
ω² = k/mass
ω² = 9 /96.52
ω² = 0.093 ..................3
we can say that from equation 2 and 3 that α² - ω² = -0.092239
this is less than zero
so differential equation is
x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
equation of motion for the mass is x(t) = e^αt ( C1 cos √{α² - ω²} t + C2 sin √{α² - ω²} t )
Answer:
the unit is m/s
Explanation:
Speed has the dimensions of distance divided by time. The SI unit of speed is the metre per second, but the most common unit of speed in everyday usage is the kilometre per hour or, in the US and the UK, miles per hour
Density = (mass/volume)
<span>Mass = # atoms (in unit cell) x (mol / 6.022 x 10^23 atoms) x (58.69 g/mol) </span>
<span>The last number is the atomic mass of nickel </span>
<span>The number of atoms = 8(1/8) + 6(1/2) = 4
</span>The volume (of the entire unit cell) = side^3 = (r x 8^(1/2))^3
<span>6.84 g/cm3 = [4 atoms x (mol / 6.022 x 10^23 atoms) x (58.69 g/mol)] / [r x 8^(1/2)]^3
</span>
<span> r = 1.36 x 10^-8 cm</span>
Answer:
t all= 30h
Explanation:
In this problem the speed of the plane is constant, so we can use the equations of uniform rectilinear motion, the definition of average speed is the distance traveled between the time taken.
v = d / t
Let's calculate each distance
First part of the trip
v₁ = d₁ / t₁
d₁ = v₁ t₁
d₁ = 120 t₁
Second part of the trip
v₂ = d₂ / t₂
d₂ = v₂ t₂
d₂ = 180 t₂
Total trip
v₃ = d₃ / t₃
d₃ = v₃ t₃
d₃ = 170 t₃
The total travel distance is the sum of each distance and the total time is the initial time of 5 h plus the time of the second part (t2)
d₁ + d₂ = 170 t₃
120 5 + 180 t₂ = 170 (5 + t₂)
Let's solve
600 + 180 t₂ = 850 +170 t₂
t₂ (180 -170) = 850 - 600
10 t₂ = 250
t₂ = 25 h
Therefore, the total travel time is
t all= 5 +25 = 30h
