Assume that you can drive at a constant speed of 100 kilometers per hour. suppose you started driving from the sun. how long wou
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Answer:
The Doppler Effect is given by the following relation;
Where;
f' = The frequency the observer hears
f = Actual frequency of the wave
v = The velocity of the sound wave
= The velocity of the observer
= The velocity of the source
Where the observer is stationary, we have;
(i) When the source is moving in the direction of the observer
(ii) When the source is receding from the observer, we have;
Therefore;
(a) A person left behind on the platform
For a person left behind on the platform, we have that the radio source is receding, therefore, we have;
(1) Given that (v + ) > v, therefore, v < (v +
), f' < f, the frequency heard by the person left on the platform, f', is smaller (lower) than the frequency produced by the radio
(2) The frequency is not constant as the speed of the source is increasing while it under the acceleration due to gravity
(3) During the fall, the speed of the source continuously increases under the effect of gravitational attraction and therefore the frequency heard by the person on the platform becomes progressively smaller
(b) A person down below floating on a rubber raft
For the the person down below on the rubber raft, the radio source is advancing
Therefore, the radio source is moving towards the person at rest down on the rubber raft, therefore, we have;
(1) Given that (v - ) < v, therefore, f' > f, the frequency heard by the person down below floating on the rubber raft, f', is greater (higher) than the frequency produced by the radio
(2) The frequency is not constant as the speed of the source is increasing while it under the acceleration due to gravity
(3) During the fall, the speed of the source continuously increases under the effect of gravitational attraction and therefore the frequency heard by the person on the platform becomes progressively greater (higher)
Explanation:
Answer:
(a) F = 0.00322i - 0.00793j with magnitude |F| = 0.00856N
(b) E = -42846.7 N/C
Explanation:
The diagram attached below explains some parameters.
Parameters given:
Charge Q1 = +50 nC at point (0, 0)
Charge Q2 = -50 nC at point (0.1, 0)
Charge Q3 = +150 nC at point (0.1, 0.08)
* The distances are in meters.
(a) The total electric force on the charge Q3 due to Q1 and Q2 is the vector sum of the forces due to Q1 and Q2. Mathematically,
F = F1 + F2
FORCE DUE TO Q1 i.e. F(Q1, Q3)
We have to find the x and y components.
From the diagram, we can find θ using SOHCAHTOA:
θ = tan⁻¹ (0.08/0.1)
θ = 38.66⁰
The distance between Q1 and Q3 can be found using Pythagoras theorem:
x² = 0.08² + 0.1²
x = 0.128 m
F1 = Fx(Q1, Q3)i + Fy(Q1, Q3)j
F1 = iF(Q1, Q3)cosθ + jF(Q1, Q3)sinθ
F(Q1, Q3) = (k * Q1 * Q3) / r²
k = Coulombs constant
F(Q1, Q3) = (9 * 10⁹ * 50 * 10⁻⁹ * 150 * 10⁻⁹) /(0.128)²
F(Q1, Q3) = 0.00412N
F1 = i0.00412 * cos38.66 + j0. 00412 * sin38.66
F1 = 0.00322i + 0.00257j N
FORCE DUE TO Q2 i.e. F(Q2, Q3)
We have to find the x and y components.
F2 = Fx(Q2, Q3)i + Fy(Q2, Q3)j
F2 = iF(Q2, Q3)cos90 + jF(Q2, Q3)cos0
F(Q2, Q3) = (k * Q2 * Q3) / r²
F(Q2, Q3) = (9 * 10⁹ * -50 * 10⁻⁹ * 150 * 10⁻⁹) /(0.08)²
F(Q2, Q3) = -0.0105N
F2 = -i0.0105 * cos90 - j0.0105 * cos0
F2 = - 0.0105j N
Hence, the total force will be
F = F1 + F2
F = 0.00322i + 0.00257j - 0.0105j
F = 0.00322i - 0.00793j N
The magnitude of this force is:
|F| = √(0.00322² + (-0.00793²)
|F| = 0.00856N
(b) The electric field at charge Q3 is the sum of the electric fields due to Q1 and Q2:
E = E1 + E2
E1, electric field due to Q1 = kQ1/r²
E1 = (9 * 10⁹ * 50 * 10⁻⁹) / (0.128²)
E1 = 27465.8 N/C
E2, electric field due to Q2 = (9 * 10⁹ * -50 * 10⁻⁹) / (0.08²)
E1 = -70312.5N/C
The total electric field:
E = E1 + E2
E = 27465.8 - 70312.5
E = -42846.7 N/C
