Physics, 13.03.2020 03:32 rafa3997

A plate drops onto a smooth floor and shatters into three pieces of equal mass. Two of the pieces go off with equal speeds v at right angles to one another. Find the speedand direction of the third piece.

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Answer from: DisneyGirl11

The plates are assumed to travel along the floor surface, such their initial

velocity along the floor plane is (zero) is used for the calculation

The speed and direction of the third piece are √2·v and 225° respectively

Reasons:

Let, m represent the mas of the plate pieces.

Let the direction of piece 1 be along the x-axis, and the direction of piece 2 be along the y-axis, we have;

$\vec{v}_1$ = v·i

$\vec{v}_2$ = v·j

Let v₃ represent the speed of piece 3

Taking the initial speed of the plate as v₁, by conservation of linear momentum, we have;

(m + m + m)·v₁ = v·i·m + v·j·m + v₃·m

Initial velocity along the horizontal x and y direction is zero, therefore;

(m + m + m)·v₁ = 0 = v·i·m + v·j·m + v₃·m

v₃·m = -(v·i·m + v·j·m)

v₃ = -(v·i + v·j)

The magnitude of the velocity of the third piece, |v₃| = √((-v)² + (-v)²) = √(2·v²)

The magnitude of the velocity of the third piece, |v₃| = √2·v

Given that the direction of the third piece is in the negative x and y directions, we have;

$\displaystyle Direction \ of \ third \ piece,\ \theta= arctan\ \left(\frac{-v}{-v} \right) =180^{\circ} + 45^{\circ} = \mathbf{225^{\circ}}$

The direction of the third piece is 225°

Learn more about the conservation of momentum principle here:

link

Answer from: Tioquino8089

Speed of the this part is given as

$v_3 = \sqrt2 v$

Also the direction of the velocity of the third part of plate is moving along 135 degree with respect to one part of the moving plate

Explanation:

As we know by the momentum conservation of the system

we will have

P_1 + P_2 + P_3 = P_i

here we know that

P_1 = P_2

the momentum of two parts are equal in magnitude but perpendicular to each other

so we will have

$P_1 + P_2 = \sqrt{P^2 + P^2}$

$P_1 + P_2 = \sqrt2 mv$

now from above equation we have

P_3 = -(P_1 + P_2)

$mv_3 = -(\sqrt 2 mv)$

$v_3 = \sqrt2 v$

Also the direction of the velocity of the third part of plate is moving along 135 degree with respect to one part of the moving plate

Answer from: Quest

The magnets would be | n s | and | s n|

Answer from: Quest

what is the actual question though?

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A plate drops onto a smooth floor and shatters into three pieces of equal mass. Two of the pieces go...

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