Answer:
The value is [tex]KE_B = 20.59 \ J[/tex]
Explanation:
From the question we are told that
The mass of the ball is [tex]m = 183 \ kg[/tex]
The initial speed of the ball is [tex]u = 18.8 \ m/s[/tex]
The spring constant is [tex]k = 86.9 \ N/m[/tex]
The compression distance is [tex]x = 0.520 \ m[/tex]
Generally the energy stored in the string is mathematically represented as
[tex]E = \frac{1}{2} * k * x^2[/tex]
=> [tex]E = \frac{1}{2} * 86.9 * 0.520 ^2[/tex]
=> [tex]E = 11.75 \ J[/tex]
Generally the kinetic energy of the ball is mathematically represented as
[tex]KE_b = \frac{1}{2} * m * u^2[/tex]
=> [tex]KE_b = \frac{1}{2} * 0.183 * (18.8 )^2[/tex]
[tex]KE_b = 32.34 \ J[/tex]
Generally the KE the ball have when it has compressed the spring is mathematically represented as
[tex]KE_B = KE_b - E[/tex]
=> [tex]KE_B = 32.34 - 11.75[/tex]
=> [tex]KE_B = 20.59 \ J[/tex]
