How Fast Will the Block Move After Being Released from the Spring?

[volraithe]

A 1.54-kg block is held against a spring of force constant 1.47E+4 N/m, compressing it a distance of 0.100 m. How fast is the block moving after it is released and the spring pushes it away?

i thought u just use the formulas that F=kx and then plug that into F=ma, but i am not getting the right answer... anyone have any other suggestions as to what path I should take?
thank you.

 

[Pengwuino]

A 1.54-kg block is held against a spring of force constant 1.47E+4 N/m, compressing it a distance of 0.100 m. How fast is the block moving after it is released and the spring pushes it away?

i thought u just use the formulas that F=kx and then plug that into F=ma, but i am not getting the right answer... anyone have any other suggestions as to what path I should take?
thank you.

Doing that will only give you the instantaneous acceleration. The problem with this is that the force will change continuously as the mass is pushed with the spring; this results in a constantly changing acceleration and we can't use our kinematics very easily. We want to use something else.

A very simple method for this problem would be to use the fact that the potential energy of the spring is \frac{{kx^2 }}{2}. We know that upon release, the spring is going to transfer all of it's energy into the mass. We of course know the energy of a mass as <br /> \frac{{mv^2 }}{2}. Equating both sides allows you to solve for the velocity of the mass.