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2 years ago

14

A thin uniform rod of mass M and length L is bent at its center so that the two segments are perpendicular to each other. Find i

ts moment of inertia about an axis perpendicular to its plane and passing through the point where the two segments meet.

1 answer:

serg [7]2 years ago

5 0

Answer:

$\frac{1}{12}ML^2$

Explanation:

The moments of the whole object is the sum of the moments of the 2 segments of rod at their ends of which length is L/2 and mass M/2:

$I = 2I_{end} = 2\frac{1}{3}\frac{M}{2}\left(\frac{L}{2}\right)^2$

$I = \frac{1}{3}M\frac{L^2}{4}$

$I = \frac{1}{12}ML^2$

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What type of plate boundary do most volcanoes occur along

sertanlavr [38]

Answer:

Subducting convergent boundary

Explanation:

Generally, volcanoes occurs in both divergent and convergent boundaries. But the convergent boundary it occurs is usually associated with subduction.

Divergent boundary, plates move away from each other creating a new crust in the process. The diverging plates creates the space for magma to be squeezed through cracks and fissures. The magma's erupt to form volcanoes. In the Atlantic ocean the spreading of the plates causes an upwelling of magma through the crest of the Atlantic ridges. New oceanic crust are formed through this process. Sometimes the magma eruption forms volcanoes that are higher than the sea level.

Convergent boundary , plates collides with each other . But in the case of volcanoes existence , the collision should be between a denser plate(oceanic plates) and a less dense plates(continental plates) so that subduction can take place. The subducted plates (oceanic plates) creates trenches and get expose to high temperature and pressure as it sinks toward the mantle. The upper mantle rocks melts and migrate to the earth surface forming volcanoes . Over 75% of the volcanoes occur along the pacific basin where convergent boundary is dominant. Pacific ring of fire has one of the most number of volcanoes.

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3 years ago

7. A mother pushes her 9.5 kg baby in her 5kg baby carriage over the grass with a force of 110N @ an angle

jasenka [17]

Weight of the carriage $=(m+M)g =142.1\ N$

Normal force $=Fsin(\theta) + W = 197.1\ N$

Frictional force $=\mu N=27.59\ N$

Acceleration $=4.66\ m\ s^{-2}$

Explanation:

We have to look into the FBD of the carriage.

Horizontal forces and Vertical forces separately.

To calculate Weight we know that both the mass of the baby and the carriage will be added.

So Weight(W) $=(m+M)\times g =(9.5+5)\ kg \times 9.8 =142.1\ Newton\ (N)$

To calculate normal force we have to look upon the vertical component of forces, as Normal force is acting vertically.We have weight which is a downward force along with $F_x$ , force of $110\ N$ acting vertically downward.Both are downward and Normal is upward so Normal force $=Summation\ of\ both\ forces$

Normal force (N) $= Fsin(\theta)+W=110sin(30) + 142.1 =197.1\ N$

Frictional force (f) $=\mu N=0.14\times 197.1 =27.59\ N$

To calculate acceleration we will use Newtons second law.

That is Force is product of mass and acceleration.

We can see in the diagram that $F_y=Horizontal$ and $F_x=Vertical$ component of forces.

So Fnet = Fy(Horizontal) - f(friction) $= m\times a$

Acceleration (a) = $\frac{Fcos(\theta)-\mu N}{mass(m)} =\frac{(95.26-27.59)}{14.5}= 4.66\ m\ s{^2 }$

So we have the weight of the carriage, normal force,frictional force and acceleration.

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2 years ago

Cassie is an engineering undergrad. She does not like talking much, and has become a quiet and withdrawn person while in her pro

stepan [7]

Answer:

A

Explanation:

Analytical people are less responsive to others. They hence tend to focus more on work than people and are less interested in leading, being happier to work by themselves. They may be prudent and systematic, making them good at analytic work.

Some character traits of Analytical people

Focuses on work and working more than people

Likes to be correct and will take time to ensure this

Thoughtful, careful fact-oriented and precise

Good at problem-solving

Likes organization and structure

Avoids working in a group, preferring to work alone

Can be over-critical and unresponsive

Cautious in decision-making

When stressed may withdraw or become headstrong

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3 years ago

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Bond [772]

Answer:

71%

Explanation:

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2 years ago

A mass m attached to a horizontal massless spring with spring constant k, is set into simple harmonic motion. its maximum displa

Lesechka [4]

At the point of maximum displacement (a), the elastic potential energy of the spring is maximum:
$U_i= \frac{1}{2} ka^2$
while the kinetic energy is zero, because at the maximum displacement the mass is stationary, so its velocity is zero:
$K_i =0$
And the total energy of the system is
$E_i = U_i+K= \frac{1}{2}ka^2$

Viceversa, when the mass reaches the equilibrium position, the elastic potential energy is zero because the displacement x is zero:
$U_f = 0$
while the mass is moving at speed v, and therefore the kinetic energy is
$K_f = \frac{1}{2} mv^2$
And the total energy is
$E_f = U_f + K_f = \frac{1}{2} mv^2$

For the law of conservation of energy, the total energy must be conserved, therefore $E_i = E_f$ . So we can write
$\frac{1}{2} ka^2 = \frac{1}{2}mv^2$
that we can solve to find an expression for v:
$v= \sqrt{ \frac{ka^2}{m} }$

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3 years ago