Show that the area under the force-time graph gives the magnitude of the
impulse of the given force for the following case when (i) force is constant
(ii) variable force.
plzz help........ irrelevant ans will be reported
Answers
Answer:
The area under the net force vs. time graph represents the change in momentum (also known as the impulse).
Answer:
(i) When constant force acts on the body:
Let constant force F acts on a body which neither changes in magnitude nor in direction with time t. In this case, the force-time graph is a straight line AB, parallel to the time-axis (Figure).
The area of the rectangle OABC = OA x OC = F x t Which is the magnitude of the impulse of a constant force F in time interval t.
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(ii) When varible force acts on the body:
Let a variable force F act on a body, which changes either in magnitude or in direction or both with time. In this case, the force-time graph is shown above.
To find the magnitude of the impulse of the variable force, divide the time-interval OB into small intervals. Each interval of time should be so small that the force during this interval may be assumed as constant.
Consider one such interval of time ab (say). Draw ad and bc perpendicular on the curve OAB. Now, we get a small strip abcd.
The area of the shaded strip abcd = ad x ab or bc x ab (here ad and bc are considered equal). This area gives the magnitude of the impulse acting on the body for the time interval ab.
To calculate the impulse of the force during the total time OB, the whole area under the curve OAB is divided into small strips gives up us the magnitude of the total impulse during the time interval OB.
Thus, the area under the force-time graph gives the magnitude of the impulse of the given force during the given time interval.