A mass attached to a spring oscillates in simple harmonic motion with an amplitude of 10 cm. When the mass is 5.0 cm from its equilibrium point, what percentage of its energy is kinetic?
To find the percentage of the energy that is kinetic when the mass is 5.0 cm from its equilibrium point, we need to calculate the total energy of the system and then determine the amount of kinetic energy.
In simple harmonic motion, the total energy of the system remains constant and is the sum of the potential energy and the kinetic energy:
Total Energy = Potential Energy + Kinetic Energy
Since the mass-spring system is oscillating, the total energy remains the same throughout the motion.
Now, let's break down the steps to find the percentage of kinetic energy at a specific point:
Step 1: Find the total energy of the system.
The total energy of a mass-spring system is given by the formula:
Total Energy (E) = (1/2) * k * A^2
where k is the spring constant and A is the amplitude of the oscillation.
Step 2: Calculate the potential energy at the given position.
The potential energy of a mass-spring system at a specific position can be calculated using the formula:
Potential Energy = (1/2) * k * x^2
where x is the displacement from the equilibrium position.
Step 3: Determine the kinetic energy.
Since the total energy remains constant, we can subtract the potential energy from the total energy to get the kinetic energy:
Kinetic Energy = Total Energy - Potential Energy
Step 4: Calculate the percentage of kinetic energy.
To find the percentage of kinetic energy, divide the kinetic energy by the total energy and multiply by 100:
Percentage of Kinetic Energy = (Kinetic Energy / Total Energy) * 100
Now, let's substitute the given values into the equations and calculate the percentage of kinetic energy.
Given:
Amplitude (A) = 10 cm
Displacement (x) = 5.0 cm
Let's assume the spring constant (k) is known or provided in the question.
Step 1: Find the total energy of the system.
Total Energy (E) = (1/2) * k * A^2
Step 2: Calculate the potential energy at the given position.
Potential Energy = (1/2) * k * x^2
Step 3: Determine the kinetic energy.
Kinetic Energy = Total Energy - Potential Energy
Step 4: Calculate the percentage of kinetic energy.
Percentage of Kinetic Energy = (Kinetic Energy / Total Energy) * 100
By following these steps and substituting the given values, you should be able to find the percentage of kinetic energy when the mass is 5.0 cm from its equilibrium point.