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 electromagnetic radiation with the shortest wavelength are gamma rays.
Explanation:
Photons are the particles that constitute light and its kwnow that lights propagates as electromagnetic waves.
The electromagnetic spectrum is the distribution of radiation due to the different frequencies at which it radiates and its different intensities, that radiation is formed by electromagnetic waves, which are transverse waves formed by an electric field and a magnetic field perpendicular to it.
The distribution of the radiation in the electromagnetic spectrum can also be given in wavelengths, but it is more frequent to work with it at frequencies, the highest being that of gamma rays, followed by X-rays, ultraviolet rays and the visible region , and those of lower frequencies, which correspond to infrared, microwave and radio waves.
The energy given for each wavelength can be found by means of the following equation.
(1)
but 

(2)
Where E is the energy, h is the planck's constant and
is the wavelength.
So, it can be see in equation 2 that when the wavelength increases the energy decreases (inversely proportional).
Hence, the electromagnetic radiation with the shortest wavelength are gamma rays.
Answer:
7 m/s²
Explanation:
The formula for force is:

We want to find acceleration, so we must rearrange the formula for
. Divide both sides of the equation by 


Acceleration can be found by dividing the force by the mass.
The force is 42 newtons and the mass is 6 kilograms. A newton is equal to 1 kg * m/s², therefore the force is 42 kg* m/s².

Substitute the values into the formula.


Divide. When we divide, the kg in the numerator and denominator will cancel each other out.


The acceleration of the object is 7 meters per square seconds.
Answer:
Explanation:
Read forces directly from the graph.
Read displacements directly from the graph.
Use the area under the graph to find the work done by the force. This is equal to the kinetic or potential energy the object gains due to the application of the force.
Answer:
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