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3 years ago

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The trap-jaw ant can snap its mandibles shut in as little as 1.3 10-4 s. In order to shut, both mandibles rotate through a 90° a

ngle. What is the average angular velocity of one of the mandibles of the trap-jaw ant when the mandibles snap shut in 2.20 10-4 s?

1 answer:

arsen [322]3 years ago

5 0

Answer

given,

Time,t = 1.3 x 10⁻⁴ s

angle of rotation = 90° = $\dfrac{\pi}{2}\ rad$

Average angular velocity of the mandible

$\omega =\dfrac{\Delta \theta}{\Delta t}$

$\omega =\dfrac{\dfrac{\pi}{2}}{1.3\times 10^{-4}}$

ω = 1.21 x 10⁴ rad/s

average angular velocity is equal to 1.21 x 10⁴ rad/s

if the time given is = 2.20 x 10⁻⁴ s

$\omega =\dfrac{\Delta \theta}{\Delta t}$

$\omega =\dfrac{\dfrac{\pi}{2}}{2.20\times 10^{-4}}$

ω = 7.14 x 10³ rad/s

average angular velocity is equal to 7.14 x 10³ rad/s

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a) (0, -33, 12)

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Explanation:

<h2>a) </h2>

We know that the cross product of linearly independent vectors $\vec{A}$ and $\vec{B}$ gives us a nonzero, orthogonal to both, vector. So, if we can find two linearly independent vectors on the plane through the points P, Q, and R, we can use the cross product to obtain the answer to point a.

Luckily for us, we know that vectors $\vec{A} = \vec{P}-\vec{Q}$ and $\vec{B} = \vec{R} - \vec{Q}$ are living in the plane through the points P, Q, and R, and are linearly independent.

We know that they are linearly independent, cause to have one, and only one, plane through points P Q and R, this points must be linearly independent (as the dimension of a plane subspace is 3).

If they weren't linearly independent, we will obtain vector zero as the result of the cross product.

So, for our problem:

$\vec{A} = \vec{P} - \vec{Q} \\\\\vec{A} = (1,0,1) - (-2,1,4)\\\\\vec{A} = (1 +2,0-1,1-4)\\\\\vec{A} = (3,-1,-3)$

$\vec{B} = \vec{R} - \vec{Q} \\\\\vec{B} = (6,2,7) - (-2,1,4)\\\\\vec{B} = (6 +2,2-1,7-4)\\\\\vec{B} = (8,1,3)$

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<h2>B)</h2>

We know that $\vec{A}$ and $\vec{B}$ are two sides of the triangle, and we also know that we can use the magnitude of the cross product to find the area of the triangle:

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According to the principle of work and kinetic energy (also known as the work-energy theorem) states that the work done by the sum of all forces acting on a particle equals the change in the kinetic energy of the particle.

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<h2>_____________________________________</h2><h2>Best Regards,</h2><h2>'Borz'</h2>

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Answer:

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