Pushing on the pump of a soap dispenser compresses a smallspring. When the spring is compressed 0.49 cm, its potential energyis 0.0025 J. (a) Whatis the force constant of thespring? kN/m? (b)What compression is required for the spring potential energy toequal 0.0083 J? cm? Pushing on the pump of a soap dispenser compresses a smallspring. When the spring is compressed 0.49 cm, its potential energyis 0.0025 J. (a) Whatis the force constant of thespring? kN/m? (b)What compression is required for the spring potential energy toequal 0.0083 J? cm?
Explanation / Answer
compression x = 0.49 cm = 0.0049 m potential energy U = 0.0025 J we know U = ( 1/ 2) k x ^ 2 from this force constant k = 2U / x ^ 2 = 208.24 N / m = 0.20824 kN / m (b). potential energy U ' = 0.0083 J ( 1/ 2) k x ' ^ 2 = 0.0083 J from this x ' = [ 2 * 0.0083 / 208.24 ] =0.008928 m = 0.8928 cm