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Andru [333]
3 years ago
15

Suppose that you needed to make a pen for some small animals. You have 12 m of fencing. You decide to make a circular pen, becau

se if you wish to enclose an area using a given length of fencing, then a circular fence encloses a larger area than a fence of any other shape. What is the radius r of the pen? Express your answer in meters to four significant figures.
Physics
1 answer:
Lady_Fox [76]3 years ago
8 0

Answer:

1.909 m

Explanation:

Length of fence = 12 m

r = Radius of circle made by the provided fence

Cirumference of a circle is given by

C=2\pi r

The circumference of the circle will be equal to the length of the fence

2\pi r=12

\\\Rightarrow r=\dfrac{12}{2\pi}

\\\Rightarrow r=1.909\ m

The radius of the fence is 1.909 m

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The centripetal force that causes the charge to move in a circular motion = The force exerted on the charge due to magnetic field

Force due to magnetic field = qvB sin θ

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v = velocity of the charge

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θ = angle between the velocity of the charge and the magnetic field = 90°, sin 90° = 1

F = qvB

Centripetal force responsible for circular motion = mv²/r = mvw

where w = angular velocity.

The centripetal force that causes the charge to move in a circular motion = The force exerted on the charge due to magnetic field

mvw = qvB

mw = qB

w = (qB/m) = (5.4 × 10⁻⁶ × 2.7)/(4.5 × 10⁻⁸)

w = 3.24 × 10² rad/s

w = 324 rad/s

w = (angular displacement)/time

Time = (angular displacement)/w

Angular displacement = π rads (half of a circle; 2π/2)

Time = (π/324) = 0.00970 s

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