Is the amount of stretch of the springs proportional to the hanging mass? Explain briefly. Derive a theoretical expression to find k-equivalent for springs in parallel and springs in series.

When connected in parallel, the extension of both springs is the same, and the total elastic force will be equal to the sum of the forces in each spring: x=x1=x2,F=F1+F2. F=F1+F2,⇒kx=k1x1+k2x2=(k1+k2)x,⇒k=k1+k2.

Given:

In the given figure the vertices of triangle ABC are A(-2,2), B(4,2), C(-2,-2).

The vertices of triangle A'B'C' are A'(-4,4), B'(8,4), C'(-4,-4).

To find:

The center of dilation and the scale factor.

Solution:

In the given graph, draw the lines AA', BB' and CC'. The intersection point of these lines is the center of dilation.

From the below graph, it is clear that the lines AA', BB' and CC' intersect each other at (0,0).

Therefore, the center of dilation is (0,0).

If a figure is dilated by factor k and the center of dilation is origin, then

It is given that A'(-4,4). So,

On comparing both sides, we get

Therefore, the scale factor is 2.