Four balls, each of mass m, are connected by four identical relaxed springs with spring constant k. The balls are simultaneously given equal initial speeds v directed away from the center of symmetry of the system as shown in (Figure 1) .
A) As the balls reach their maximum displacement, their kinetic energy reaches __. (Choices are, A=maximum; B=Zero; C= Neither maximum nor zero.
B) Each of the balls will move outwards to a maximum displacement d, from its initial position. Use geometry to find x, the distance each of the springs has stretched from its equilibrium position. (It may help to draw the initial and the final states of the system.)
Please help
1 Answer
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A) B
B) Each ball is reacted by a spring constant K = 2k in the x & y direction. Their vector sum along the direction of v is K√2 = k2*√2
Equating the initial KE to the final SE,
½mv² = ½(2√2k)x² → x = v*√[m/k]/√[2√2]
I think