Please show work Thank you A 300g object connected to a spri

Please show work. Thank you.

A 30.0-g object connected to a spring with a force constant of 40.0 N/m oscillates with an amplitude of 8.00 cm on a frictionless, horizontal surface.

(a) Find the total energy of the system.


(b) Find the speed of the object when its position is 1.30 cm. (Let 0 cm be the position of equilibrium.)

At this point the energy is partially stored as potential energy of the spring and partially as kinetic energy of the object. m/s

(c) Find the kinetic energy when its position is 3.50 cm.

You should be solving this problem without considering the mass of the object. mJ

(d) Find the potential energy when its position is 3.50 cm.

Solution

a)

Total Energy of the system

E_T=(1/2)KA² = (1/2)40*0.08²

E_T=0.128 J

b)

Since

E_T =(1/2)mV²+(1/2)Kx²

0.128 =(1/2)[0.03*V²+40*0.013²]

0.03V² = 0.24924

V=2.88 m/s

c)

E_T =(1/2)mV²+(1/2)Kx²

0.128 =(1/2)[0.03*V²+40*0.035²]

V=2.63m/s

Kinetic energy

KE=(1/2)mV²=(1/2)*0.03*2.63² =0.1035 J

d)

Potential energy

U=(1/2)KX²=(1/2)*40*0.035²

U=0.0245 J