The electron relaxation time is
The mean free path is
<u>Explanation:</u>
Electron density,
Aluminium resistivity,
From the Drude's model we have:
Where:
τ= Electron relaxation time
m = mass of a charge
q = magnitude of a charge
We know, electron mass =
Charge of electron =
By substituting all given values for electron, we get
When multiply by 100 and divide by 100, we get
Mean free path is given as:
where:
l = Mean free path
= Average velocity of electrons
We know the general value for average velocity of electrons at room temperature:
Therefore,
Answer:
Object 3 has greatest acceleration.
Explanation:
Objects Mass Force
1 10 kg 4 N
2 100 grams 20 N
3 10 grams 4 N
4 1 kg 20 N
Acceleration of object 1,
Acceleration of object 2,
Acceleration of object 3,
Acceleration of object 4,
It is clear that the acceleration of object 3 is and it is greatest of all. So, the correct option is (3).
Answer:
42000N
Explanation:
First you calculate how much it would contract, and secondly you then calculate the force to stretch it by that amount.
1) linear thermal expansion coef brass 19e-6 /K
∆L = αL∆T = (19e-6)(1.85)(110) = 0.00387 meter or 3.87 mm
Second part involves linear elasticity.
for brass, young's modulus is 15e6 psi or 100 GPa
cross-sectional area of rod is π(0.008)² = 0.0002 m²
F = EA∆L/L
F = (100e9)(0.0002)(0.00387) / (1.85)
F = 42000 or 42 kN
Answer:
Explanation:
a ) F = (-kx + kx³/a²)
intensity of field
I = F / m
= (-kx + kx³/a²) / m
If U be potential function
- dU / dx = (-kx + kx³/a²) / m
U(x) = ∫ (kx - kx³/a²) / m dx
= k/m ( x²/2 - x⁴/4a²)
b )
For equilibrium points , U is either maximum or minimum .
dU / dx = x - 4x³/4a² = 0
x = ± a.
dU / dx = x - x³/a²
Again differentiating
d²U / dx² = 1 - 3x² / a²
Put the value of x = ± a.
we get
d²U / dx² = -2 ( negative )
So at x = ± a , potential energy U is maximum.
c )
U = k/m ( x²/2 - x⁴/4a²)
When x =0 , U = 0
When x= ± a.
U is maximum
So the shape of the U-x curve is like a bowl centered at x = 0
d ) Maximum potential energy
put x = a or -a in
U(max) = k/m ( x²/2 - x⁴/4a²)
= k/m ( a² / 2 - a⁴/4a²)
= k/m ( a² / 2 - a²/4)
a²k / 4m
This is the maximum total energy where kinetic energy is zero.