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Anni [7]
3 years ago
11

When the acceleration of a mass on a spring is zero, the velocity is at a

Physics
1 answer:
Sergeu [11.5K]3 years ago
6 0

1) Maximum

2) Maximum

Explanation:

The force acting on a mass on a spring is given by Hooke's law; in magnitude:

F=kx

where

F is the force

k is the spring constant

x is the displacement

Also we know from Newton's second law that we can write

F=ma

where

m is the mass

a is the acceleration

So we can write the equation as

ma=kx (1)

From this relationship, we see that the acceleration is directly proportional to the displacement.

On the other hand, we know that the total mechanical energy of the system mass-spring is constant, and it is given by

E=\frac{1}{2}kx^2+\frac{1}{2}mv^2=const. (2)

where the first term is the elastic potential energy while the second term is the kinetic energy, and where

v is the velocity of the mass

From eq. (2), it is clear that when displacement increases, velocity decreases, and vice-versa; however, from eq.(1) we also know that acceleration is proportional to the displacement.

Therefore this means that:

- When acceleration increases, velocity decreases

- When acceleration decreases, velocity increases

Therefore, the two answers here are:

- When the acceleration of a mass on a spring is zero, the velocity is at a  maximum

When the velocity of a mass on a spring is zero, the acceleration is at a  maximum

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