If a toy train uses all its mechanical energy to compress a spring, what is the compression distance if the spring constant is 1.00 × 10^5 N/m?

To find the compression distance of the spring when the mechanical energy of the toy train is entirely transformed into potential energy stored in the spring, we can use the formula for elastic potential energy stored in a spring:

[ PE = \frac{1}{2} k x^2 ]

where ( PE ) is the potential energy, ( k ) is the spring constant, and ( x ) is the compression distance of the spring.

If we assume that the initial mechanical energy of the toy train is completely converted into this potential energy, we can set up the equation as follows:

[ E_{initial} = \frac{1}{2} k x^2 ]

From this, we can solve for ( x ):

[ x = \sqrt{\frac{2E_{initial}}{k}} ]

Assuming the initial mechanical energy, ( E_{initial} ), is known or can be calculated separately, plugging in the given spring constant of ( 1.00 \times 10^5 ) N/m allows for the determination of ( x ).

For the option marked as 0.0119 m to be the correct answer, it must have arisen from plugging reasonable values for ( E_{initial}