Answer: the expression of the mechanical energy for under damped system is;
x(t)=Ae−γ/2tcos(ωdt+ϕ), where ωd=ω02−γ2/4
γ = damping rate, and
ω0 = the angular frequency of the oscillator without damping.
Explanation:
The physical situation in mechanical energy defined through out the world has three possible results depending on the value of a (which is a constant value), which depends on the value of what is under our radical. This expression can either be positive, negative, or equal to zero which will result in overdamping, underdamping, and critical damping, as the case may be.
γ2 >4ω²0 This is the Over Damped case. Here, the system returns to equilibrium by exponentially decaying towards zero, and the system will not pass that equilibrium position more than once.
γ² < 4ω²0 this is the Under Damped case. Here, the system moves back and forth as it slowly returns to equilibrium and the amplitude of the system decreases over time.
Finally, γ² = 4ω²0
This is the Critically Damped case. Here, the system returns to equilibrium very fast without moving back and forth and without passing the equilibrium position at all.
Answer:
A. Attractive
B. ( μ₀I² ) / ( 2πd )
Explanation:
A. We know that currents in the same direction attract, and currents in the opposite direction repel, according to ampere's law. In this case the current in the two wires are flowing in the same direction, and hence the force between the two wires are attractive.
B. Suppose that two wires of length and both carry the current in the same direction ( given ). In the presence of a magnetic field produced by wire 1, a force of magnitude m say, is experienced by wire 2. The magnitude of the magnetic field produced by wire 1 at distance say d, from it's axis, should thus be the following -
= μ₀I / 2πd
The force experienced by wire 2 should thus be -
= I( )
= I Sin( 90 )
= I ( μ₀I / 2πd )
Therefore the force per unit length experienced by wire 2 toward wire 1 should be ...
( / ) = ( μ₀I² ) / ( 2πd ) ... which is our solution
Answer:
The 43kg student will be sliding at 1.79m/s opposite the direction the 34kg student is going.
Explanation:
Conservation of linear momentum!
The law of conservation of momentum says that in an isolated system, the momentum before must equal the momentum after:
.
For our two students
(notice the - sign in -2.4m/s, this means going to the left)
since the students were not moving at first, , therefore we have
solving for gives
Hence the 43kg student will be sliding at 1.79m/s to the right.
Answer:
1.4 billion light years away
Explanation:
v = Recessional velocity = 30000 km/s[/tex]
= Hubble constant =
D = Distance to the galaxy
According to Hubble's law
The galaxy is 1.4 billion light years away