Question

a spring gun can give a ball kinetic energy K when compressed by x. If compressed by 2x, what kinetic energy can it give to the ball?

Answer 1

`\begin{gathered} K_(2x)=4K \\ or \\ K_(2x)=2kx^2 \end{gathered}`

Step-by-step explanation

The kinetic energy of a spring is equivalent to the elastic potential energy, which means that the kinetic energy of a spring is given as:

`K=(1)/(2)\cdot k\cdot x^2`

where k = spring constant

x = amount of compression

Therefore, when the compression is 2x, the kinetic energy it can give the ball is:

`\begin{gathered} K_(2x)=(1)/(2)\cdot k\cdot(2x)^2 \\ K_(2x)_{}=(1)/(2)\cdot k\cdot4x^2 \\ K_(2x)=4((1)/(2)\cdot k\cdot x^2)\Rightarrow2kx^2 \\ \Rightarrow K_(2x)=4K \end{gathered}`