Question

The 60.0 g mass, attached to a light spring with a 40.0 N/m force constant, vibrates with an amplitude of 5.00 cm on a horizontal, frictionless plane. find (a) the total energy of the pulsating System, (b) the speed of mass when the displacement is 2.00 cm. When the displacement is 2.50 cm, (c) the kinetic energy and (d) the potential energy

Answer 1

Step-by-step explanation:

(a) The total energy is the elastic potential energy at maximum displacement.

E = ½ kx²

E = ½ (40.0 N/m) (0.0500 m)²

E = 0.05 J

(b) At this displacement, there is both elastic potential energy and kinetic energy.

E = EE + KE

0.05 J = ½ kx² + ½ mv²

0.05 J = ½ (40.0 N/m) (0.0200 m)² + ½ (0.060 kg) v²

v = 1.18 m/s

(c) E = EE + KE

0.05 J = ½ kx² + ½ mv²

0.05 J = ½ (40.0 N/m) (0.0250 m)² + KE

KE = 0.0375 J

(d) EE = ½ kx²

EE = ½ (40.0 N/m) (0.0250 m)²

EE = 0.0125 J