Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring?The maximum kinetic energy and maximum potential energy are equal, but occur at different times.The maximum kinetic energy occurs at the maximum displacement of the mass from its equilibrium positionThe maximum potential energy is achieved when the mass passes through its equilibrium position.The kinetic and potential energies are equal to each other at all times.Clear my choice
Question
Which of the following is true for a system consisting of a mass oscillating on the end of an ideal spring?The maximum kinetic energy and maximum potential energy are equal, but occur at different times.The maximum kinetic energy occurs at the maximum displacement of the mass from its equilibrium positionThe maximum potential energy is achieved when the mass passes through its equilibrium position.The kinetic and potential energies are equal to each other at all times.Clear my choice
Solution
The correct statement is: "The maximum kinetic energy and maximum potential energy are equal, but occur at different times."
Here's why:
-
In a system of a mass oscillating on an ideal spring, the energy of the system is conserved, meaning it is constant. The energy of the system is a combination of kinetic energy (the energy of motion) and potential energy (the energy of position).
-
The maximum kinetic energy occurs when the mass is passing through its equilibrium position. At this point, the mass is moving at its maximum speed, and thus has the maximum kinetic energy.
-
The maximum potential energy occurs when the mass is at its maximum displacement from the equilibrium position. At this point, the spring is stretched or compressed the most, and thus has the maximum potential energy.
-
The kinetic and potential energies are not equal to each other at all times. They are constantly changing as the mass oscillates. When one is at a maximum, the other is at a minimum.
So, the first statement is the correct one.
Similar Questions
Which of the following statements is not true regarding a mass-spring system that moves with simple harmonic motion in the absence of friction?The potential energy stored in the system is greatest when the mass passes through the equilibrium position.The energy of the system is continually transformed between kinetic and potential energy. The velocity of the oscillating mass has its maximum value when the mass passes through the equilibrium position.The total energy of the system remains constant.The total energy of the system is proportional to the square of the amplitude.
A mass-spring oscillating system undergoes SHM with maximum amplitude A. If the spring constant is doubled what effect will it produce on the mechanical energy of the system
The total mechanical energy of a spring - mass system in simple harmonic motion is 𝐸=12𝑚𝜔2𝐴2. Suppose the oscillating particle is replaced by another particle of double the mass while the amplitude 𝐴 remains the same. The new mechanical energy will
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?
Two blocks each of the mass 𝑚 areconnected to a spring of spring constant𝑘. If both are given velocity 𝜐 in oppositedirections, then the maximumelongation of the spring is
Upgrade your grade with Knowee
Get personalized homework help. Review tough concepts in more detail, or go deeper into your topic by exploring other relevant questions.