If the rate of change of the magnetic field applied to a loop of wire is doubled, what happens to the induced emf in that loop a
1 answer:
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<h2>Answer:</h2>
Torque = <em>2.05 x 10²⁸ Nm</em>
Energy = <em>3.54 x 10³³ J</em>
Average power = <em>1.02 x 10²⁸ W</em>
<h2>Explanation:</h2>(a) Torque (τ) is the rotational effect of a given force.
It is given by
τ = I x α -------------(i)
Where;
I = rotational inertia of the object
α = angular acceleration of the object.
In this case, the object is the Earth. Therefore,
I = 9.71 x 10³⁷ kg m²
α = ω / t
Where;
ω = angular velocity of earth = 2π rad / day
<em>Since </em>
<em>1 day = 24 hours and 1 hour = 3600seconds</em>
<em>1 day = 24 x 3600 seconds = 86400seconds</em>
<em>=> ω = 2π rad / 86400seconds</em>
<em>=> ω = 7.29 × 10⁻⁵ rad/s</em>
<em />
t = 4 days = 4 x 24 x 3600 seconds = 345600 seconds
=> α = ω / t
=> α = 7.29 × 10⁻⁵ / 345600
=> α = (7.29 × 10⁻⁵) / (3.456 x 10⁵)
=> α = (7.29 × 10⁻⁵⁻⁵) / (3.456)
=> α = (7.29 × 10⁻¹⁰) / (3.456)
=> α = 2.11 × 10⁻¹⁰ rad/s²
Now substitute the values of I and α into equation (i)
τ = 9.71 x 10³⁷ x 2.11 × 10⁻¹⁰
τ = 9.71 x 10²⁷ x 2.11
τ = 20.5 x 10²⁷ Nm
τ = 2.05 x 10²⁸ Nm
(ii) The energy (rotational energy) E is given by;
E = x I x ω
E = x 9.71 x 10³⁷ x 7.29 × 10⁻⁵
E = 35.4 x 10³² J
E = 3.54 x 10³³ J
(iii) The average power P, is given by;
P = E / t
P = 3.54 x 10³³ / 345600
P = 1.02 x 10²⁸ W
Answer:
t = 2.01 s
Vf = 19.7 m/s
Explanation:
It's know through the International System that the earth's gravity is 9.8 m/s², then we have;
Data:
- Height (h) = 20 m
- Gravity (g) = 9.8 m/s²
- Time (t) = ?
- Final Velocity (Vf) = ?
==================================================================
Time
Use formula:
Replace:
Everything inside the root is solved first. So, we solve the multiplication of the numerator:
It divides:
The square root is performed:
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Final Velocity
use formula:
- Vf = g * t
Replace:
- Vf = 9.8 m/s² * 2.01 s
Multiply:
- Vf = 19.7 m/s
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How long does it take to reach the ground?
Takes time to reach the ground in <u>2.01 seconds.</u>
How fast does it hit the ground?
Hits the ground with a speed of <u>19.7 meters per seconds.</u>