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.
Answer:
The central blue square in between the lower pair of magnet has the least force of repulsion.
Explanation:
We can explain this using the dual nature of magnets.
Each magnet must have two poles namely:
-North pole
-South pole
We assume that the magnetic lines of forces enters from south pole and leaves from the north pole.
When brought together, like poles repel each other while opposite poles attract each other.
In the picture, the lower two magnets have opposite poles facing each other, hence the force of repulsion is minimum there and the force of attraction is maximum.
8.16m is the required height, a 5kg stone need to be raised.
One sort of potential energy is gravitational potential energy, which is equal to the product of the object's mass (m), the gravitational acceleration (g), and the object's height (h) as measured in relation to the ground's surface (the body).
We obtain the formula by considering the work done in raising a mass m through a height h.
Work in elevating mass m through height h is equal to force times distance.
The force must be greater than the mass m's weight, hence F = mg.
Work done = mgh = gravitational potential energy
Energy = Mass of the object × gravitational acceleration × height.
Mass of the stone = 5kg
Equating ;
∴ 400 J = 5 kg × 9.8 m/s² × height
Height = 8.16 m
Therefore, 8.16m is the required height.
Learn more about energy here:
brainly.com/question/1242059
#SPJ1
Answer: f = - 0.50 m, negative (diverging) lens
Explanation: D-value (diopter ) means 1/f, unit is 1/m. Thus -2.0D
Means f = ( 1/ -2.0 ) m = -0.50 m