Suppose a ball obliquely strikes a rough horizontal surface then it experiences a frictional impulse and conservation of linear momentum cannot be done on the horizontal direction.

Now consider another setup in which one block is resting on a rough horizontal surface and another block moving towards the 1st block collides with it. Then is the momentum of the system conserved? I think that it should not be conserved because the value of friction acting on the system (combination of the 2 blocks) changes from zero to a non zero value. But in books I have seen that they apply conservation of linear momentum. Why do we consider frictional impulse in 1st setup and neglect frictional impulse in the second one?


1 Answer 1


We consider friction to an impulsive force, in cases when normal force is impulsive. Here's how:

We know that $f=\mu N$(only during slipping motion, for no slipping frictional force is equal to applied force RESISTING friction). Since friction is proportional to normal reaction, it will be impulsive only when normal force is impulsive.

Thus, if in a situation there is a sudden change in normal force, friction will be impulsive( part of reason why a water ballon or mud ball burst or distort when thrown to ground, because of impulsive friction due to impulsivee normal force.)

Therefore, in your question, since normal is impulsive in case 1 , momentum cant be conserved, but it can be done in case 2 because no extra force, tending to make normal force impulsive acts on system.

  • $\begingroup$ If we consider the block at rest: Just before collision friction is not proportional to normal force as it has no tendency to move. But during collision it experiences friction, which is static I suppose, which is again does not depend on normal force. So why does the normal come into play when deciding whether the friction will be impulsive or not? $\endgroup$ Commented Apr 21, 2016 at 3:35
  • $\begingroup$ becuase the formula for friction(during slipping) is dependent upon normal force, and for no slliping there will be no force acting(in this case). $\endgroup$
    – oops
    Commented Apr 21, 2016 at 4:06
  • $\begingroup$ For no slipping static friction acts which is a force not dependent on normal. There is a frictional force acting. Isn't it? $\endgroup$ Commented Apr 21, 2016 at 5:40
  • $\begingroup$ It may only happen, if force is applied. If no force, then no friction.By that, I mean forces that tend to produce motion $\endgroup$
    – oops
    Commented Apr 21, 2016 at 5:41
  • $\begingroup$ Thats why I specifically mentioned "during slipping". $\endgroup$
    – oops
    Commented Apr 21, 2016 at 5:44

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