Question

A .183 kg ball is moving 18.8 m/s when it runs into a spring of spring constant 86.9 N/m. How much KE does the ball have when it has compressed the spring 0.520 m? (Unit=J)

Answer 1

Answer:

The value is  $KE_B = 20.59 \ J$

Explanation:

From the question we are told that

   The mass of the ball is  $m = 183 \ kg$

   The initial  speed of the ball is  $u = 18.8 \ m/s$

    The spring constant is  $k = 86.9 \ N/m$

     The compression distance is  $x = 0.520 \ m$

Generally the energy stored in the string is mathematically represented as

        $E = \frac{1}{2} * k * x^2$

=>     $E = \frac{1}{2} * 86.9 * 0.520 ^2$

=>      $E = 11.75 \ J$

Generally the kinetic energy of the ball is mathematically represented as

          $KE_b = \frac{1}{2} * m * u^2$

=>      $KE_b = \frac{1}{2} * 0.183 * (18.8 )^2$

        $KE_b = 32.34 \ J$

Generally the KE   the ball have when it has compressed the spring is mathematically represented as

          $KE_B = KE_b - E$

=>        $KE_B = 32.34 - 11.75$

=>        $KE_B = 20.59 \ J$