Respuesta :
Answer:
Speed of the this part is given as
[tex]v_3 = \sqrt2 v[/tex]
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
[tex]P_1 + P_2 + P_3 = P_i[/tex]
here we know that
[tex]P_1 = P_2[/tex]
the momentum of two parts are equal in magnitude but perpendicular to each other
so we will have
[tex]P_1 + P_2 = \sqrt{P^2 + P^2}[/tex]
[tex]P_1 + P_2 = \sqrt2 mv[/tex]
now from above equation we have
[tex]P_3 = -(P_1 + P_2)[/tex]
[tex]mv_3 = -(\sqrt 2 mv)[/tex]
[tex]v_3 = \sqrt2 v[/tex]
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
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;
[tex]\vec{v}_1[/tex] = v·i
[tex]\vec{v}_2[/tex] = 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;
[tex]\displaystyle Direction \ of \ third \ piece,\ \theta= arctan\ \left(\frac{-v}{-v} \right) =180^{\circ} + 45^{\circ} = \mathbf{225^{\circ}}[/tex]
- The direction of the third piece is 225°
Learn more about the conservation of momentum principle here:
https://brainly.com/question/11953231
