Disadvantages of magnets
1 answer:
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<h2>Answer:</h2>
(e) halved
<h2>Explanation:</h2>The electrical enery (E) stored in a capacitor is related to its capacitance (C) and potential difference (V) as follows;
E = x C x
------------------------(i)
Also, the capacitance (C) of a capacitor consisting of parallel plates is related to the area (A) of the plates and distance (d) between the plates as follows;
C = A x ε₀ / d ------------------------(ii)
Where;
ε₀ is the permittivity of free space.
Substituting equation (ii) into equation (i) gives;
E = x A x ε₀ / d x
--------------------(iii)
From equation(iii)
When the potential difference (V) is constant, then the electrical energy (E) stored is <em>inversely </em>proportional to the distance between the plates. i.e
E = k / d ----------------(iv)
Where;
k = proportionality constant = x A x ε₀ x
(which is the product of all constants)
Therefore from equation (iv);
=> E₁ x d₁ = E₂ x d₂ ---------------------------(v)
Where;
E₁ and E₂ are the initial and final values of the electrical energy stored.
d₁ and d₂ are the initial and final values of the distance between the plates.
<em>So, when the distance is doubled, i.e.</em>
d₂ = 2 x d₁
<em>Substitute the value of d₂ into equation (v) to give;</em>
=> E₁ x d₁ = 2 x d₁ x E₂
<em>Divide through by d₁ to give;</em>
=> E₁ = 2 x E₂
<em>Make E₂ subject of the formula</em>
=> E₂ = x E₁
Therefore, the electrical energy stored in the capacitor will be halved.
Answer: The final speed, ignoring the effects of friction, will be 2.88 m/s.
Explanation:
The problem can be solved using two different physical principles. If we resort to Newton's second Law, we can say that, neglecting friction (which is reasonable for a ice block) the only force acting on the block in the direction of the movement along the plane, is the component of the weight that is parallel to the slope, i.e.
Fp = mg sin 28.3º = ma ⇒ a=g sin 28.3º
Now, as we know that g = constant, we can use the following kinematic equation:
vf² - v₀² = 2 a x
if the block starts from rest, this means that v₀ = 0.
Replacing by the values in the equation, and solving for vf, we get;
vf = = 2.88 m/s
The other approach is using the conservation of energy principle:
When the block starts, it has some potential energy = mgh
This height h, can be expressed in terms of x (the length travelled by the block downward the plane) and the angle that forms with the horizontal, as follows:
h = x sin 28.3 (applying sin definition) ⇒ U = mg x sin 28.3
At the the end of the slide, the potential energy has been converted to kinetic energy, so we can write the following equation:
m. g. x. sin 28.3º = 1/2 m vf²
Simplifying, replacing by the values and solving for vf, we arrive to the same result as above.