An aerobatic airplane pilot experiences weightlessness as she passes over the top of a loop the loop maneuver. The acceleration
1 answer:
The radius of the loop is 18.9 km
Explanation:
When the airplane is at the top of the loop, the pilot experiences two forces:
- The force of gravity, acting downward, of magnitude
- The normal reaction exerted by the seat on the pilot, also acting downward, N
Since the plane is moving in a circular motion, the net force on the pilot must be equal to the centripetal force, therefore we can write:
where
m is the mass of the pilot
is the acceleration of gravity
N is the normal reaction
v = 430 m/s is the speed of the plane
r is the radius of the loop
Here we are told that the pilot feel weightless at the top of the loop: this means that the normal reaction is zero,
N = 0
Therefore the equation becomes
And so we can find the radius of the loop:
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Answer:
0.5
Explanation:
The energy of a charged capacitor is given by where
is the charge on it and
is its capacitance. The capacitance is defined, geometrically, as
where is a constant that is determined by the material between the plates,
is the area of the plates and
is the distance between them. It is then that the capacitance is linearly inversely proportional to the separation distance; as the distance increases, the capacitance reduces.
Because it is linear, when the separation distance is doubled, other factors remaining constant, the capacitance is halved. Because the capacitance is halved, the energy is halved.
Let's see the mathematics.
Initial capacitance, at initial separation,
If separation is doubled, separation becomes . Then the capacitance becomes
Initial energy,
Final energy,
Hence,