Answer:
a) V = k 2π σ (√(b² + x²) - √ (a² + x²))
,
b) E = - k 2π σ x (1 /√(b² + x²) - 1 /√(a² + x²))
Explanation:
a) The expression for the electric potential is
V = k ∫ dq / r
For this case, consider the disk formed by a series of concentric rings of radius r and width dr, the distance of each ring to point P
R = √(x² + r²)
The charge on a ring is
σ = dq / dA
The area of a ring is
A = π r
dA = 2π r dr
So the charge is
dq = σ 2π r dr
We substitute
V = k σ 2pi ∫ r dr / √(r² + x²)
We integrate
V = k 2π σ √(r² + x²)
We evaluate from the lower limit r = a to the upper limit r = b
V = k 2π σ (√(b² + x²) - √ (a² + x²))
b) the electric field and the potential are related
E = - dV / dx
E = - k 2π σ (1/2 2x /√(b² + x²) - ½ 2x /√(a² + x²))
E = - k 2π σ x (1 /√(b² + x²) - 1 /√(a² + x²))
Given: Initial velocity of toy car (u ) = 0
Final velocity of toy car (v) = 0.12 m/s
Required time (t) = 0.1 s
To find: The acceleration of the toy car.
Let the acceleration of the toy car be (a)
Formula Used: 1st kinematic equation of motion
v = u + at ---------------------------(i)
Here, all alphabets are in their usual meanings
Now, from equation (i), we shall calculate the value of 'a'.
so, a = (v - u) /t
or, a = (0.12 m/s - 0) / 0.1s
or, a = 1.2 m/s²
Hence, the required acceleration of the toy car will be 1.2 m/s².
Answer:
51.2 J, 86.2 J, 137.4 J
Explanation:
The kinetic energy of the ball is given by:
where
m = 0.40 kg is its mass
v = 16 m/s is its speed
Substituting,
The potential energy of the ball is given by
where
m = 0.40 kg
is the acceleration of gravity
h = 22 m is the heigth of the cliff
Substituting,
Finally, the total mechanical energy is the sum of the kinetic energy and the potential energy:
Answer:
wash your hands and social distance
Explanation:
