Question

Question #f3570

Answer 1

Dependent on amplitude and
Conserved

Explanation:

Mechanical energy is the sum of Kinetic energy and Potential energy.
`E_o=K+U`

Imagine an object moving in a circle with constant angular velocity, `omega`.

Let displacement, `x=Asin(omegat)`
`v=(dx)/(dt)=Aomegacos(omegat)`

The kinetic energy,`K` is `1/2mv^2= 1/2mA^2omega^2cos^2(omegat)`
Maximum kinetic energy will be accompanied by zero potential energy:
`E_o=K_max+U_min`
`=K_max`
Therefore, `K_max=1/2mA^2omega^2cos^2(2pi)=1/2mA^2omega^2`
and since `E_o=K_max`,

`E_o=1/2mA^2omega^2`

From the equation above, I conclude that mechanical energy is:

• Dependent on amplitude
• Dependent on mass
• Conserved (`E_o` is just a multiplication of constants as derived above)