The maximum kinetic energy of the mass can be found using the principle of conservation of energy. This principle states that the total energy of the system is conserved, meaning it remains constant.

In this case, the total energy of the system is the sum of the kinetic energy and the potential energy. The kinetic energy is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. The potential energy stored in the spring is given by the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement.

At the maximum displacement (x = 2.0 cm = 0.02 m), the velocity of the mass is zero, so all the energy is potential energy. We can calculate this as follows:

PE = 1/2 * k * x^2 = 1/2 * 9.0 N/m * (0.02 m)^2 = 0.0018 Joules.

Since the total energy is conserved, this is also the maximum kinetic energy of the mass. So, the maximum kinetic energy of the mass is 0.0018 Joules.

Question

The maximum kinetic energy of the mass can be found using the principle of conservation of energy. This principle states that the total energy of the system is conserved, meaning it remains constant.

In this case, the total energy of the system is the sum of the kinetic energy and the potential energy. The kinetic energy is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. The potential energy stored in the spring is given by the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement.

At the maximum displacement (x = 2.0 cm = 0.02 m), the velocity of the mass is zero, so all the energy is potential energy. We can calculate this as follows:

PE = 1/2 * k * x^2 = 1/2 * 9.0 N/m * (0.02 m)^2 = 0.0018 Joules.

Since the total energy is conserved, this is also the maximum kinetic energy of the mass. So, the maximum kinetic energy of the mass is 0.0018 Joules.

Knowee AI · Accepted Answer

The maximum kinetic energy of the mass can be found using the principle of conservation of energy. This principle states that the total energy of the system is conserved, meaning it remains constant.

In this case, the total energy of the system is the sum of the kinetic energy and the potential energy. The kinetic energy is given by the formula KE = 1/2 * m * v^2, where m is the mass and v is the velocity. The potential energy stored in the spring is given by the formula PE = 1/2 * k * x^2, where k is the spring constant and x is the displacement.

At the maximum displacement (x = 2.0 cm = 0.02 m), the velocity of the mass is zero, so all the energy is potential energy. We can calculate this as follows:

PE = 1/2 * k * x^2 = 1/2 * 9.0 N/m * (0.02 m)^2 = 0.0018 Joules.

Since the total energy is conserved, this is also the maximum kinetic energy of the mass. So, the maximum kinetic energy of the mass is 0.0018 Joules.

A 1.0 kg mass is connected to a spring with a spring constant of 9.0 N/m. If the initial velocity is 4.0 cm/s and the initial displacement is 2.0 cm, then what is the maximum kinetic energy of the mass?

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