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 mass of the sign is 44.5 kg.
Explanation:
Given that,
Force acting on the sign, F = 445 N
We need to find the mass of the sign.
Net force acting on it is given by :
F = mg
Where g is the acceleration due to gravity
So, the mass of the sign is 44.5 kg.
Density is mass over volume:
In your case, mass is 48 grams and volume is 12cm^3
If you put that into the equation, you will get your density:
Answer
given,
mass of the ski = 75 Kg
speed of the skier, v = 3 m/s
time = 1.50 min = 90 s
angle of inclination, θ = 40°
distance = s x t
= 3 x 90 = 270 m
a) W = F. d cos θ
W = mg. d cos θ
W = 75 x 9.8 x 270 x cos 40°
W = 152021.52 J
work is done by the ski lift is equal to 152021.52 J
b) Power extended by the ski
P = 1689.13 Watt.
power is expended by the ski lift is equal to 1689.13 W.
D. Ted associated being asked a question with embarrassment.