physics mechanics qu (1 Viewer)

[velox]

You are asked to design spring bumpers for the walls of a parking garage. A freely rolling m car moving at v is to compress the spring no more than x before stopping.

What should be the force constant of the spring? Assume that the spring has negligible mass.

I thought it would be 1/2mv^2 / x but apparently that is not right. Anyone know what I should be doing?

 

[alcalder]

This is the equation for working out the spring force constant. (Hooke's Law)

<table border="0" align="center" cellpadding="0" cellspacing="0"> <tbody><tr><td>F_x</td> <td> = </td> <td>force</td> </tr> <tr> <td>k</td> <td> = </td> <td>spring force constant</td> </tr> <tr> <td>x</td> <td> = </td> <td>distance from equilibrium </td> </tr> <tr> <td>x₀</td> <td> = </td> <td>spring equilibrium position</td></tr></tbody> </table>


And Spring Potential energy.

Using your data then perhaps you want the kinetic energy of the car equal to the sprint pring potential energy and that will stop it.

1/2 mv² = 1/2 kx²

k = mv²/x²