12.5 J.
The answer is 12.5 J or D.
Answer:
Explanation:
Given that, .
Frequency
f = 60Hz
Number of turns
N = 125turns
Surface area of coil
A = 3 × 10^-2 m²
Magnetic field
B = 0.12T
Voltage peak to peak? I.e the EMF
EMF is given as
ε = —dΦ/dt
Where Φ is magnetic flux and it is given as
Φ = NBA Cosθ
Where N is number of turns
B is magnetic field
A is the cross sectional area
And θ is the resulting angle from the dot product of area and magnetic field
Where θ =ωt and ω = 2πf
Then, θ = 2πft
So, your magnetic flux becomes
Φ = NBA Cos(2πft)
Now, dΦ / dt = —NBA•2πf Sin(2πft)
dΦ / dt = —2πf • NBA Sin(2πft)
So, ε = —dΦ/dt
Then,
ε = 2πf • NBA Sin(2πft)
So, the maximum peak to peak emf will occur when the sine function is 1
I.e Sin(2πft) = 1
So, the required peak to peak emf is
ε = 2πf • NBA
Substituting all the given parameters
ε = 2π × 60 × 125 × 0.12 × 3 × 10^-2
ε = 169.65 Volts
The peak to peak voltage is 169.65 V
The minimum initial velocity that the ball must have for it to reach the top of the hill is 21 m/s. The correct option is D.
<h3>What is mechanical energy?</h3>
The mechanical energy is the sum of kinetic energy and the potential energy of an object at any instant of time.
M.E = KE +PE
A boy is trying to roll a bowling ball up a hill. The friction is ignored. The ball must have to reach the top of the hill with a velocity. The acceleration due to gravity, g = 9.8 m/s²
The conservation of energy principle states that total mechanical energy remains conserved in all situations where there is no external force acting on the system.
M.E bottom of hill = M.E on top of hill
Kinetic energy + Potential energy = Kinetic energy + Potential energy
1/2 mu² + 0 = 0 + mgh
At the top of hill, the velocity will become zero. So, final kinetic energy is zero.
Substituting the values, we have
1/2 x u² = 9.8 x 22.5
u = sqrt [2 x9.8 x 22.5 ]
u= 21 m/s
Thus, the minimum initial velocity that the ball must have for it to reach the top of the hill is 21 m/s.
Learn more about mechanical energy.
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It often requires STANDARD reaction time