The above figure depicts a ball of mass m which is equipped on its lower side...

  

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The above figure depicts a ball of mass m which is equipped on its lower side with a massless spring of uncompressed length Lo and spring constant k. The spring is initially compressed to a length L < Lo, as shown in the figure. The ball-spring system is either dropped vertically or launched with a horizontal speed to from a height of ho at a distance ro from a wall of height hw. The spring remains compressed until it touches the ground. When it touches the ground the spring is released (by a mechanism not shown on the figure) and expands very quickly back to its uncompressed length Lo and is then held fixed at length Lo. The bounce of the ball-spring system on the ground is assumed to be totally elastic. (a) When the ball is dropped vertically, find the maximum height hmar the ball- spring system could reach after its bounce in terms of the spring's compression AL = LoL, and the parameters m, g, k and ho. In analogy to ho in the figure, hmar should be the vertical distance between the floor and the lower end of the spring after the bounce. You may take g = 10 ms ¹. (b) Find the optimal value for the distance ro from which the ball would bounce over a wall with maximum value of hw.. [3] [6] hw-ho Хо Vo ho The above figure depicts a ball of mass m which is equipped on its lower side with a massless spring of uncompressed length Lo and spring constant k. The spring is initially compressed to a length L < Lo, as shown in the figure. The ball-spring system is either dropped vertically or launched with a horizontal speed to from a height of ho at a distance ro from a wall of height hw. The spring remains compressed until it touches the ground. When it touches the ground the spring is released (by a mechanism not shown on the figure) and expands very quickly back to its uncompressed length Lo and is then held fixed at length Lo. The bounce of the ball-spring system on the ground is assumed to be totally elastic. (a) When the ball is dropped vertically, find the maximum height hmar the ball- spring system could reach after its bounce in terms of the spring's compression AL = LoL, and the parameters m, g, k and ho. In analogy to ho in the figure, hmar should be the vertical distance between the floor and the lower end of the spring after the bounce. You may take g = 10 ms ¹. (b) Find the optimal value for the distance ro from which the ball would bounce over a wall with maximum value of hw.. [3] [6] hw-ho Хо Vo ho

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a mgho b mg hoAL 1 kAt mg hmay LoL mg no AL 9 kal mghman ... View the full answer