A 1.9 kg object that stretches a spring 8.2 cm from its natural length when hang

ID: 1550784 • Letter: A

Question

A 1.9 kg object that stretches a spring 8.2 cm from its natural length when hanging at rest oscillates with an amplitude of 3.4 cm.

a. Find the total energy of the system. The acceleration due to gravity is 9.81 m/s2. Answer in units of J. 024

b. Find the gravitational potential energy at maximum downward displacement. Answer in units of J. 025

c. Find the potential energy in the spring at maximum downward displacement. Answer in units of J. 026

d. What is the maximum kinetic energy of the object? Answer in units of J.

(a)

K*x= m*g

K = 1.9*9.81/0.082=227.30 N/m

Total energy of the spring:

E= 1/2*K*xmax^2 +m*g*x(when it is stretched extremely)

=0.5*227.30*0.034^2 +1.9*9.81*0.034=0.765 J.

(b)

gravitational potential energy at maximum downward displacement =E =m*g*h = 0.634 J

(c)

potential energy in the spring at maximum downward displacement = 1/2*k*Xmax^2 = 0.1314 J

(d)

Maximum kinetic energy, KE= E

= 1/2*K*xmax^2 +m*g*x

=0.5*227.30*0.034^2 +1.9*9.81*0.034=0.765 J.

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