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Consider a plank on a frictionless surface and a ball from a height H is dropped on this plank. There is no friction between the plank and ball. Can the plank jump up in air for any value of H?

I don't want to know the value of H for which would happen. I just want to know that is this even possible that the plank jumps due to the normal impulse being greater than the collision impulse. This is no numerical, just a conceptual doubt.

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This is an interesting question.

An ideal plank (rigid, much heavier than the ball) will not rebound, but a real plank has some elasticity - either in the material itself or as a structure (eg if the plank is supported at the ends and the middle is raised off the ground). If a heavy solid object is dropped onto it, it will rebound to some extent and jump off its supports.

This is an example of a multiple collision : body A collides with body B which collides with body C. Here body C is the Earth. Except for ideal situations and materials, it is very difficult to predict whether B will lift off the ground and how far. But you would need to know much more than simply the height from which A is dropped.

Apart from the masses of the ball m and plank M and the height H from which the ball is dropped, you also need to know something about the elasticity of each collision (A-B and B-C). This is related to how much kinetic energy is lost during the collision and is conveniently expressed in terms of the Coefficient of Restitution which is defined as :

e = relative speed of separation / relative speed of approach.

A similar problem (Bouncing Superballs) is solved in the following links (p 15 in the first link) : http://web.mit.edu/8.01t/www/materials/modules/chapter15.pdf http://hep.physics.wayne.edu/~harr/courses/2130/f99/demonstration1.htm


UPDATE after you addition to the question :

Yes, this is definitely possible. I have seen it happen myself when a brick has been dropped onto a plank. Try it for yourself using eg a tennis ball and a ruler.

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  • $\begingroup$ To simplify the cases let us take a ball of mass m dropped from a height H on an ideal plank(rigid).of mass 2m. Can the plank jump for any value of H? $\endgroup$ Commented May 8, 2016 at 17:03
  • $\begingroup$ @user1825567 : Are you asking for a particular purpose? If so, please can you edit your question to include more details, as it helps to know the context. Also, please can you show your attempt to solve this problem, because I need to know what your level of understanding is. It is not the purpose of this site to solve problems for you, or to provide tuition, but to help you to solve your own problems. So we need to see what effort you have made to solve this problem. $\endgroup$ Commented May 9, 2016 at 1:43
  • $\begingroup$ Please se the question again, I have made a conceptual request $\endgroup$ Commented May 10, 2016 at 14:37
  • $\begingroup$ @user1825567 : Thank you. I have updated my answer also. $\endgroup$ Commented May 10, 2016 at 14:55
  • $\begingroup$ This experience is when we are dealing with real objects. I want to know whether this can happen theoretically when we are taking ideal objects and solving like general physics problem by drawing FBD(Force Body Diagram) . I hope you understood my doubt. $\endgroup$ Commented May 10, 2016 at 15:32

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