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A rectangular plate is rotating with a constant angular speed about an axis that passes perpendicularly through one corner, as the drawing shows. The centripetal acceleration measured at corner A is n times as great as that measured at corner B. What is the ratio
L1
L2
of the lengths of the sides of the rectangle when n = 2.24?

Sagot :

varshamittal029

The ratio of L1 and L2 ,lengths of the sides of the rectangle when n = 2.24 is 2.0043

We use the centripetal acceleration definition,  

[tex]a = \frac{v^2}{r}[/tex]

The relationship between angular and linear velocity

[tex]v=w^2r[/tex]

we substitute [tex]a = w^2 r[/tex]

The rectangular body rotates at an angle of w.

We locate the points, but the diagram is missing. In this case, the axis of rotation is in a corner called O, one of the adjacent corners is called A, and the opposite corner is called B.

the distance[tex]OB = L_2[/tex]

the distance [tex]AB = L_1[/tex]

It is indicated that the accelerations in A and B are related, so we substitute the acceleration value.

   [tex]w^2 r_A = n r_B[/tex]

the distance from the each corner is  

 [tex]r_B = L_2\\\\ r_A =\sqrt{L_1^2+L_2^2}[/tex]

we substitute  

[tex]\sqrt{L_1^2 + L_2^2} = n L_2[/tex]

[tex]L_1^2 + L_2^2 = n^2 L_2^2[/tex]

[tex]L_1^2= (n^2-1) L_2^2\\\\\frac{L_1^2}{L_2^2}=(n^2-1)\\\\\frac{L_1}{L_2}=\sqrt{(n^2-1)}[/tex]

When n=2.24

[tex]\frac{L_1}{L_2}=\sqrt{(2.24^2-1)}\\\\\frac{L_1}{L_2}=2.0043[/tex]

Thus, the ratios of length is 2.0043.

To learn more about centripetal acceleration refer here

https://brainly.com/question/14465119

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