Question

A block strikes the free end of a horizontal spring with thethe free end of a horizontal spring with the other end fixed, placed on a smooth surfacewith a speed v. After compressing the spring by x, the speed of the block reducompression of the spring.the spring by x, the speed of the block reduces to half. Calculate the maximum compression of the spring​

Answer 1

Answer:

The maximum compression in the spring is given

$x_m = \sqrt{\frac{4}{3}}x$

Explanation:

By work energy theorem we know that

Work = change in kinetic energy

$0 - \frac{1}{2}k x^2 = \frac{1}{2}m(\frac{v}{2})^2 - \frac{1}{2}mv^2$

$- \frac{1}[2}kx^2 = -\frac{3}{8}mv^2$

so we have

$\frac{1}{2}mv^2 = \frac{2}{3}kx^2$

Now to find the maximum compression we have

$\frac{1}{2}kx_m^2 = \frac{1}{2}mv^2$

now from above two equation

$\frac{4x^2}{3x_m^2} = 1$

$x_m = \sqrt{\frac{4}{3}}x$

#Learn

Topic : Work and energy of spring

https://brainly.in/question/9355842