Answer:
C1 + C2 = 30 parallel connection
C1 * C2 / (C1 + C2) = 7.2 series connection
C1 * C2 = 7.2 * (C1 + C2) = 216
C2 + 216 / C2 = 30 using first equation
C2^2 + 216 = 30 C2
C2^2 - 30 C2 + 216 = 0
C2 = 12 or 18 solving the quadratic
Then C1 = 18 or 12
Answer:
The distance from the top of the stick would be 2l/3
Explanation:
Let the impulse 'FΔt' acts as a distance 'x' from the hinge 'H'. Assume no impulsive reaction is generated at 'H'. Let the angular velocity of the rod about 'H' just after the applied impulse be 'W'. Also consider that the center of percussion is the point on a bean attached to a pivot where a perpendicular impact will produce no reactive shock at the pivot.
Applying impulse momentum theorem for linear momentum.
FΔt = m(Wl/2), since velocity of center of mass of rod = Wl/2
Similarly applying impulse momentum theorem per angular momentum about H
FΔt * x = I * W
Where FΔt * x represents the impulsive torque and I is the moment of inertia
F Δt.x = (ml² . W)/3
Substituting FΔt
M(Wl/2) * x = (ml². W)/3
1/x = 3/2l
x = 2l/3
When an object moves its length contracts in the direction of motion. The faster it moves the shorter it gets in the direction of motion.
The object in this question moves and then stops moving. So it's length first contracts and then expands to its original length when the motion stops.
The speed doesn't have to be anywhere near the speed of light. When the object moves its length contracts no matter how fast or slow it's moving.
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:120.3676
Explanation: using the molecular calculator and molar mass of MgSO4. hope this helps!
