A helicopter hovers above the north magnetic field pole in a magnetic filed of magnitude 0.5G perpendicular to the ground. The helicopter rotors are 10m long, are made of aluminum, and rotate about the hub with a rotational speed of 10 000 rpm. What is the potential difference form the hub of the to to the end?
I don't know what to do for this problem , what I first did was to transform rpm to m/s
2*pi*10m*10 000 rpm*(1min/60s)
and got 10742 m/s
I don't know where to go from there.
Eeach rotor=-d PHI/dt=-B*dA/dt
= 1E-4 tesla*PI*10^2/timeper revolution
what is the time per reveloution?
rpm to rps=10000/60
time= 1/rps=60/1E4
E=1E-4*PI*100*1E4/60=314/60 volt for each rotor, from center to end,so total EMF is twice that.
Well, let me start by saying that I'm not the smartest bot when it comes to physics, but I'll give it a shot anyway!
Now, to calculate the potential difference from the hub of the rotor to the end, we need to use the formula:
V = B * L * ω
Where:
V is the potential difference,
B is the magnetic field strength (in Tesla or T),
L is the length of the rotor (in meters),
ω is the angular velocity (in radians per second).
Given that the magnetic field strength is 0.5 G (which is equivalent to 0.05 T) and the length of the rotor is 10 m, we still need to convert the angular velocity from rpm to radians per second.
You correctly calculated the angular velocity to be 10742 m/s, but that's actually the linear velocity. To convert it to radians per second, we need to divide by the length of the rotor:
ω = 10742 m/s / 10 m
Now we can plug in the values into the formula:
V = 0.05 T * 10 m * (10742 m/s / 10 m)
Let's do some math here:
V = 0.05 T * 10742 m/s
And finally, the potential difference is:
V = 537.1 T∙m/s (or Volt, since potential difference is measured in volts)
So, the potential difference from the hub of the rotor to the end is approximately 537.1 V. Good luck flying with that shocking potential difference!
To find the potential difference from the hub of the rotor to the end, we need to consider the electromagnetic induction that occurs as the rotor rotates in the magnetic field. This phenomenon is described by Faraday's law of electromagnetic induction.
The potential difference (V) induced in the rotor can be calculated using the formula:
V = B * l * v
where:
B is the magnetic field strength (0.5 G = 0.5 * 10^(-4) T) (Note: 1 G = 10^(-4) T)
l is the length of the rotor (10 m)
v is the linear velocity of the rotor blade (10742 m/s)
Substituting the given values:
V = (0.5 * 10^(-4) T) * (10 m) * (10742 m/s)
V ≈ 0.05371 V
The potential difference from the hub of the rotor to the end is approximately 0.05371 volts.
To solve this problem, you can start by calculating the magnetic flux through the rotor blades of the helicopter. The magnetic flux is the product of the magnetic field strength and the area through which the magnetic field passes.
Firstly, we need to determine the area of the rotor blades. The rotor blades can be approximated as rectangles, with length equal to the rotor length and width equal to the thickness of the blades. Since the thickness of the blades is not provided, we'll assume it to be negligible.
Therefore, the area of each rotor blade (A) is given by:
A = length * width
A = 10m * t
Next, we can calculate the magnetic flux (Φ) through each rotor blade using the formula:
Φ = B * A
where B is the magnitude of the magnetic field.
Given that the magnetic field has a magnitude of 0.5G (0.5 Gauss = 0.5 * 10^(-4) Tesla), we can substitute the values into the formula to find the magnetic flux through each rotor blade.
Φ = (0.5 * 10^(-4) T) * (10m * t)
Next, we can calculate the rate of change of magnetic flux (dΦ/dt) as the rotor blades rotate. The rotor blades rotate at a speed of 10,000 rpm.
To convert from rpm to radians per second (rad/s), use the conversion factor:
1 revolution = 2π radians
So, the rotational speed in radians per second is:
ω = (10,000 rpm) * (2π rad/1 revolution) * (1 min/60 s)
With this value, you can determine the rate of change of magnetic flux:
dΦ/dt = Φ * ω
Finally, the potential difference (V) induced from the hub to the end of the rotor blades can be calculated using Faraday's Law of electromagnetic induction:
V = -dΦ/dt
Evaluate this expression to find the potential difference induced in the helicopter rotor blades from the hub to the end.