question_answer 49)

  Using second law of motion, derive the relation between force and acceleration. A bullet of 10 g strikes a sand-bag at speed of and gets embedded after travelling 5 cm. Calculate (i) the resistive force exerted by the sand on the bullet. (ii) the time taken by the bullet to come to rest.

Answer:

  If a body of mass (m), moving at velocity (u) accelerates uniformly at.(a) for time 'f, so that its velocity changes to v, then initial momentum and final momentum Change in momentum According to the second law of motion, force                                                                                    [where,] Here,                                                    Given,   and (i) From third equation of motion,                                                            Now, force applied, by the bullet,  F = ma [negative sign shown against the direction of motion] The resistive force exerted by the sand on the bullet = 105 N (i)From first equation of motion, v = u + at                           at = v - u Now, time taken by bullet to come to rest.                                                                                  Hence, force (F) = 105 N and time