Question

A 0.4 kg object that stretches a spring 8.8 cm from its natural length when hanging at rest oscillates with an amplitude of 4.1 cm. Find the total energy of the system. The acceleration due to gravity is 9.81 m/s2. Answer in units of J.

Answer 1

The total energy of the system is0.0375 J

Step-by-step explanation:

Given;

mass of the object, m = 0.4 kg

extension of the spring, x = 8.8 cm = 0.088 m

Amplitude of the oscillation, A = 4.1 cm = 0.041 m

Total energy of the system, is the sum of all the mechanical energy which include Kinetic energy and potential energy.

E = K + U

At maximum displacement, Vₓ = 0, the total energy is entirely potential.

E = U = ¹/₂KA²

F = kx

k = F/x

k = (mg)/x

k = (0.4 x 9.81)/0.088

k = 44.591 N/m

E = ¹/₂KA² = ¹/₂ x 44.591 x (0.041)²

E = 0.0375 J

Therefore, the total energy of the system is 0.0375 J