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 particle will be rendered still
Explanation:
The particle will be rendered still because of the Newton’s 1st law of motion states that a body will continue to move on forever until contacted by an equal and opposite force. The same case has been produced here and it is justifying the law. If the Force has another direction and magnitude than 10 N then the body will continue to move on in the direction of the greater force.
A, b and d
Competition for fix resources of course increases the
energy expenditure needed to gather those resources and leaves less for a
given population. A lower amount of sunlight or water also contributes
to decreased energy which lowers growth. Finally, small borders limit
growth in that population density can only go so high before the death
rate increases beyond the birth rate.
Negative - when the motorcycle displacement has a component in the opposite direction of the given force, that force is doing negative work on the motorcycle.
