Answer:
, the minus meaning west.
Explanation:
We know that linear momentum must be conserved, so it will be the same before (
) and after (
) the explosion. We will take the east direction as positive.
Before the explosion we have 
.
After the explosion we have pieces 1 and 2, so 
.
These equations must be vectorial but since we look at the instants before and after the explosions and the bomb fragments in only 2 pieces the problem can be simplified in one dimension with direction east-west.
Since we know momentum must be conserved we have:
Which means (since we want 
and 
):
So for our values we have:
Answer:
(a) 1462.38 m/s
(b) 2068.13 m/s
Explanation:
(a)
The Kinetic energy of the atom can be given as:
K.E = (3/2)KT
where,
K = Boltzman's Constant = 1.38 x 10⁻²³ J/k
K.E = Kinetic Energy of atoms = 343 K
T = absolute temperature of atoms
The K.E is also given as:
K.E = (1/2)mv²
Comparing both equations:
(1/2)mv² = (3/2)KT
v² = 3KT/m
v = √[3KT/m]
where,
m = mass of Helium = (4 A.M.U)(1.66 X 10⁻²⁷ kg/ A.M.U) = 6.64 x 10⁻²⁷ kg
v = RMS Speed of Helium Atoms = ?
Therefore,
v = √[(3)(1.38 x 10⁻²³ J/K)(343 K)/(6.64 x 10⁻²⁷ kg)]
<u>v = 1462.38 m/s</u>
(b)
For double temperature:
T = 2 x 343 K = 686 K
all other data remains same:
v = √[(3)(1.38 x 10⁻²³ J/K)(686 K)/(6.64 x 10⁻²⁷ kg)]
<u>v = 2068.13 m/s</u>
Answer:
E = 1000 x
Explanation:
The electric potential and the electric field are related by the formula
dV = - E . dx
Bold represents vectors.
The point represents the scalar product, in this case we calculate the electric field in the x-axis and the potential is also in this axis so the scalar product is reduced to the algebraic product
E = dV /dx
Let's make the derivative
E = - 2ax
Let's replace the values
E = -2 (-500) x
E = 1000 x
Answer:
(A) 654.545 Kw
(B) 
Explanation:
We have given resistance of the toaster 
Resistance of nichrome heating element 
Both the resistances are connected in series so same current will flow through the circuit
Potential difference across the toaster V = 120 volt
So current 
(a) Power dissipated in toaster 
(B) Power dissipated in heating element 
Answer with explanation:
The Normalization Principle states that
Given
Thus solving the integral we get
The integral shall be solved using chain rule initially and finally we shall apply the limits as shown below
Applying the limits and solving for A we get
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