Final answer:
The ratio of kinetic energy to total energy when the displacement is 10 cm is 0.
Step-by-step explanation:
To find the ratio of kinetic energy to total energy, we need to calculate the potential energy of the spring at a displacement of 10 cm.
The potential energy of a spring is given by the formula:
U = (1/2)kx^2
where U is the potential energy, k is the spring constant, and x is the displacement from the equilibrium position.
Given that the mass is 2.0 kg and the spring constant is 800 N/m, the potential energy at a displacement of 10 cm (0.1 m) is:
U = (1/2)(800 N/m)(0.1 m)^2 = 4 J
The total energy of the system is the sum of the potential energy and the kinetic energy. At any point in the oscillation, the total energy remains constant:
E = U + KE
Since we know the potential energy is 4 J, we can find the kinetic energy:
E = 4 J + KE
To find the kinetic energy, we can use the equation:
KE = (1/2)mv^2
where m is the mass and v is the velocity.
At a displacement of 10 cm, the object is at the maximum displacement and momentarily at rest. Therefore, the kinetic energy is zero.
The ratio of kinetic energy to total energy is:
Ratio = KE/E = 0/4 = 0