5. Annie drags her little red wagon with a mass of 5.00 kg, up a hill that has an angle of
1 answer:
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Answer:
(a) 2.5 m/s
(b) 37.5 KJ
Explanation:
(a)
From the law of conservation of momentum, Initial momentum=Final momentum
and making
the subject then
and since
is initial velocity of car, value given as 4 m/s,
is the initial velocity of the three cars stuck together, value given as 2 m/s and
is the final velocity which is unknown. By substitution
(b)
Initial kinetic energy is given by
Final kinetic energy is given by
The energy lost is given by subtracting the final kinetic energy from the initial kinetic energy hence
Energy lost=350-312.5=37.5 KJ
Answer:
L = μ₀ n r / 2I
Explanation:
This exercise we must relate several equations, let's start writing the voltage in a coil
= - L dI / dt
Let's use Faraday's law
E = - d Ф_B / dt
in the case of the coil this voltage is the same, so we can equal the two relationships
- d Ф_B / dt = - L dI / dt
The magnetic flux is the sum of the flux in each turn, if there are n turns in the coil
n d Ф_B = L dI
we can remove the differentials
n Ф_B = L I
magnetic flux is defined by
Ф_B = B . A
in this case the direction of the magnetic field is along the coil and the normal direction to the area as well, therefore the scalar product is reduced to the algebraic product
n B A = L I
the loop area is
A = π R²
we substitute
n B π R² = L I (1)
To find the magnetic field in the coil let's use Ampere's law
∫ B. ds = μ₀ I
where B is the magnetic field and s is the current circulation, in the coil the current circulates along the length of the coil
s = 2π R
we solve
B 2ππ R = μ₀ I
B = μ₀ I / 2πR
we substitute in
n ( μ₀ I / 2πR) π R² = L I
n μ₀ R / 2 = L I
L = μ₀ n r / 2I