Answer:
The compression is [tex]x = 0.05 \ m[/tex]
Explanation:
From the question we are told that
The first velocity is v
The compression of the spring is [tex]d = 1.0 \ cm = 0.01 \ m[/tex]
The second velocity is 4v
Generally according to the law of energy conservation
The kinetic energy of the block is equal to the energy stored in the spring that is
[tex]\frac{1}{2} * m* v^ 2 = \frac{1}{2} * k * d^2[/tex]
For first speed
[tex]m* v^ 2 = k * 0.01^2[/tex]
=> [tex]m* v^ 2 = k * 0.0001[/tex]
=> [tex]k = \frac{ m v^2 }{ 0.0001}[/tex]
For second speed
[tex]\frac{1}{2} * m* (5v)^ 2 = \frac{1}{2} * k * x^2[/tex]
=> [tex]12.5mv^2 = 0.5 k x^2[/tex]
substituting for k
=> [tex]12.5mv^2 = 0.5 (\frac{mv^2}{0.0001} ) x^2[/tex]
=> [tex]12.5 = 5000x^2[/tex]
=> [tex]x = 0.05 \ m[/tex]
