Three balls, each of mass 0.300 kg, are connected by three identical springs, wi

Question

Three balls, each of mass 0.300 kg, are connected by three identical springs, with spring constants k = 163 N/m. At i=0, the balls are simultaneously given equal initial speeds v = 1.40 m/s directed away from the centre of symmetry of the system. The springs are initially at their equilibrium Iength,x0 = 0.100m. Select true or false for the statements below; e.g., if the first statement is true and the rest false, enter TFFFF. i. In the initial configuration of the system at t = 0, the kinetic energy is a maximum. ii. In the initial configuration of the system, the spring potential energy is a maximum. iii. The distance moved by any ball is proportional to the change in length of any spring. The proportionality constant can be determined by geometry. iv. As the balls reach their maximum displacement, the spring potential energy reaches a minimum. v. As the balls reach their maximum displacement, their kinetic energy reaches zero.

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

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

FALSE

In the initial configuration of the system at t = 0, the potential eneryg is maximum

potential energy U = 0.k*x^2

at the minimum displacement x is minimum U is minimum

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

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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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TRUE

As the balls reach their maximum displacement, their kinetic energy reaches zero

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

at maximum displacement x = A

K is zero

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