Question

A 10 cm wide box is held between two springs in a 1 m gap on a frictionless surface. The left spring has a natural length of 80 cm and spring constant of 200 N/m. The right spring has a natural length of 90 cm and spring constant of 350 N/m. How far is the center of the box from the left edge in m

Answer 1

Answer:

The distance is  $x =0.291 \ m$

Explanation:

From the question we are told that

     The width of the box is $b = 10 \ cm = \frac{10}{100} = 0.10 \ m$

     The gap is of length $l = 1\ m$

    The natural length of the first spring is $y = 80 \ cm = \frac{80 }{100} = 0.8 \ m$

     The spring constant of the first spring is  $k_1 = 200 N/m$

     The second spring has a natural length of $z = 90 \ cm = \frac{90}{100} = 0.9 \ m$

      The spring constant of the first spring is  $k_2 = 350 \ N/m$

Let the distance from the center of the box to the left edge be x

      So at equilibrium

The force applied by the first spring is

      $F_1 = k_1 * (0.8 -x)$

and

The force applied by the second spring is

        $F_2 = k_2 * [ 0.9 - (0.9 -x)]$

Now at equilibrium

       $F_1 = F_2$

So

     $k_1 * (0.8 -x) = k_2 * [ 0.9 - (0.9 -x)]$

    substituting values

      $200 * (0.8 -x) = 350 * [ 0.9 - (0.9 -x)]$

        =>   $160 -200x) = 350x$

        =>  $160 =550x$

          =>   $x =0.291 \ m$