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What is the difference between a sudden force which continues to act on the body, and an impulsive force?

What would be respective speeds of the body just after time= 0?


marked as duplicate by AccidentalFourierTransform, John Rennie newtonian-mechanics Apr 22 '16 at 7:03

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In both cases, the speed of the body at time $t=0$ would be zero, if it was initially at rest. Then you will ask, what is the difference between an impulsive force and an "ordinary force" which keeps acting continuously?

Actually, there is no fundamental difference between them. But when we say impulsive force, we mean that the force is of very large magnitude, and acts for a very short interval of time (on normal timescales). An "ordinary force" acts for a significant amount of time and has a relatively small magnitude (around the values typically given in physics problems). These graphs will make it clearer:

The first one is of an impulsive force, and the second one of an ordinary force.

  • $\begingroup$ Thanx for such an useful response ! $\endgroup$ – ABC123 Apr 22 '16 at 5:34
  • $\begingroup$ But i want to ask what would be the respective velocities of the object just after t=0 in both cases ? $\endgroup$ – ABC123 Apr 22 '16 at 5:35
  • $\begingroup$ @ABC123 We can't give an exact value without knowing the impulsive force as a function of time. But we might compare their value. First draw the acceleration time graphs for impulsive force and ordinary force cases. Take some time $t$ and find the area under the graph for both cases. Whichever has greater area will have greater velocity! $\endgroup$ – FreezingFire Apr 22 '16 at 6:52
  • $\begingroup$ but i believe that an ordinary force does not change the velocity of the object at lim t->0+ (t=time) and an impulsive force does to a sufficiently observable velocity , Am i right ? $\endgroup$ – ABC123 Apr 22 '16 at 9:03
  • $\begingroup$ Calculating a limit here tells you that as you approach $t=0$, you get the velocity approaching zero, in both cases. So a limit is useless here. But to answer your question, take the graphs in my answer. You can find a value of $t>0$ where the area under both the graphs is equal (meaning equal velocity). Before that time, the velocity would actually be more for the non impulsive force. After that, the impulsive force would have greater velocity. $\endgroup$ – FreezingFire Apr 22 '16 at 10:17

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