Four balls, each of mass 0.400 kg, are connected by four identical springs, with

Question

Four balls, each of mass 0.400 kg, are connected by four identical springs, with spring constants k = 175 N/m. At t=0, the balls are simultaneously given equal initial speeds v = 4.50 m/s directed away from the centre of symmetry of the system. The springs are initially at their equilibrium length, x0 = 0.160 m. Select true or false for the statements below; e.g., if the first statement is true and the rest false, enter TFFFF.

In the initial configuration of the system at t=0, the kinetic energy is a minimum.

As the balls reach their maximum displacement, the spring potential energy reaches a maximum.

In the initial configuration of the system, the spring potential energy is zero.

The distance moved by any ball is equal to the change in length of any spring.

As the balls reach their maximum displacement, their kinetic energy reaches a minimum.

Explanation / Answer

In the initial configuration of the system at t = 0, the kinetic energy is a minimum.

FALSE

at t = 0 kinetic energy = 0.5*m*v^2 which is maximum

+++++++++++++++++++

TRUE

As the balls reach their maximum displacement, the spring potential energy reaches a maximum.

potential energy U = 0.k*x^2

at the maximum displacement x is maximum so U is maximum

-------------------------

In the initial configuration of the system, the spring potential energy is zero.

at the initial x = 0

U = 0

TRUE

---------------------

FALSE
The distance moved by any ball is equal to the change in length of any spring.

-----------------

TRUE

As the balls reach their maximum displacement, their kinetic energy reaches a minimum

kinetic energy at any point is given by k = 0.5*m*w^2*(A^2-x^2)

at maximum displacement x K is minimum

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