Answer:
Explanation:
a )
Amplitude A = 14 mm , angular frequency ω = 2π / T
= 2π / .5
ω = 4π rad /s
φ₀ = initial phase
Putting the given values in the equation
14 = 25 cos(ωt + φ₀ )
14/25 = cosφ₀
φ₀ = 56 degree
x(t) = 25cos(4πt + 56° )
b )
maximum velocity = ω A
= 4π x 25
100 x 3.14 mm /s
= 314 mm /s
At x = 0 ( equilibrium position or middle point , this velocity is achieved. )
maximun acceleration = ω² A
= 16π² x A
= 16 x 3.14² x 25
= 3943.84 mm / s²
3.9 m / s²
It occurs at x = A or at extreme position.
Answer:
s = 1.7 m
Explanation:
from the question we are given the following:
Mass of package (m) = 5 kg
mass of the asteriod (M) = 7.6 x 10^{20} kg
radius = 8 x 10^5 m
velocity of package (v) = 170 m/s
spring constant (k) = 2.8 N/m
compression (s) = ?
Assuming that no non conservative force is acting on the system here, the initial and final energies of the system will be the same. Therefore
• Ei = Ef
• Ei = energy in the spring + gravitational potential energy of the system
• Ei = \frac{1}{2}ks^{2} + \frac{GMm}{r}
• Ef = kinetic energy of the object
• Ef = \frac{1}{2}mv^{2}
• \frac{1}{2}ks^{2} + (-\frac{GMm}{r}) = \frac{1}{2}mv^{2}
• s = 
s = 
s = 1.7 m
Answer:
Explanation:
Work in pumping water from the tank is given as
W = ∫ y dF. From a to b
Where dF is the differential weight of the thin layer of liquid in the tank, y is the height of the differential layer
a is the lower limit of the height
b is the upper limit of the height.
We know that, .
F = ρVg
Where F is the weight
ρ is the density of water
V is the volume of water in tank
g is the acceleration due to gravity
Then,
dF = ρg ( Ady)
We know that the density and the acceleration due to gravity is constant, also the base area of the tank is constant, only the height that changes.
Then,
ρg = 62.4 lbs/ft³
Area = L×B = 3 × 9 = 27ft²
dF = ρg ( Ady)
dF = 1684.8dy
The height reduces from 12ft to 0ft
Then,
W = ∫ y dF. From a to b
W = ∫ 1684.8y dy From 0 to 12
W = 1684.8y²/2 from 0 to 12
W = 842.4 [y²] from y = 0 to y = 12
W = 842.4 (12²-0²)
W = 121,305.6 lb-ft
Answer:
if the image is on the book yes , no its can be both
Explanation:
B is the answer to your question
