Question

Mateo adds two labels to the Venn diagram shown to explain how velocity and acceleration change during simple harmonic motion.

Label 1: Zero at the equilibrium position
Label 2: Increases with increasing net force

Q: Where should Mateo place the labels?

A) Label 1: Z
Label 2: Z
B) Label 1: X
Label 2: Z
C) Label 1: Y
Label 2: Y
D) Label 1: Z
Label 2: X

Answer 1

I think it might be

Label 1: Z
Label 2: Z

Correct me if I'm wrong.

Answer 2

A) Label 1: Z

Label 2: Z

Step-by-step explanation:

Let's analyze separately velocity and acceleration in a simple harmonic motion.

1) Velocity:

In a simple harmonic motion, velocity is maximum at the equilibrium position, and it decreases as the system moves away from the equilibrium position. This can be understood by the law of conservation of energy: in fact, the total mechanical energy is the sum of kinetic and potential energy

`E=K+U=(1)/(2)mv^2+(1)/(2)kx^2`

where m is the mass, v the velocity, k the spring constant and x the displacement of the system from the equilibrium position. Since E must be remain constant, we can see that:

- when x=0 (equilibrium position), K is maximum, so the velocity v is maximum

- when x increases, the velocity decreases

Therefore, both label 1 and 2 are not valid for velocity.

2) Acceleration:

In a simple harmonic motion, acceleration is maximum when the displacement is maximum, and zero when the system is at equilibrium position. This is due to the fact that acceleration is proportional to the force, and the force is

`F=-kx`

so, the force F is proportional to the displacement x. Therefore:

- when x=0 (equilibrium position), the acceleration is zero

- when x increases, F increases, and so the acceleration increases as well

Therefore, both label 1 and 2 are valid for the acceleration. So, they should be placed both in Z.