A 0.00600-kg bullet traveling horizontally with speed 1.00 103 m/s strikes a 19.
ID: 1493568 • Letter: A
Question
A 0.00600-kg bullet traveling horizontally with speed 1.00 103 m/s strikes a 19.7-kg door, embedding itself 12.0 cm from the side opposite the hinges as shown in the figure below. The 1.00-m wide door is free to swing on its frictionless hinges. (a) Before it hits the door, does the bullet have angular momentum relative the door's axis of rotation? Yes No (b) If so, evaluate this angular momentum. (If not, enter zero.) kg · m2/s If not, explain why there is no angular momentum. (c) Is mechanical energy of the bullet-door system constant in this collision? Answer without doing a calculation. Yes No (d) At what angular speed does the door swing open immediately after the collision? rad/s (e) Calculate the total energy of the bullet-door system and determine whether it is less than or equal to the kinetic energy of the bullet before the collision. KEf = J KEi = J
Explanation / Answer
a) Yes.
Angular momentum = m (v x r) = m |v| |r| sin@
where @ is angel between V and r vector.
@ = 90 deg and neither of quantity is zero hence bullet have angular momentum relative door axis.
b) angular momentum = 0.006 x 1 x 10^3 x 0.12 = 0.72 kg m^2 s
c) Yes. Net torque is zero during collision.
hence angular momentum will be conserved.
d) Applying angular momentum conservation,
0.72 = I_total wf
0.72 = [( M L^2 / 3 ) + (m r^2) ] wf
0.72 = [ (19.7 x 1^2 /3) + (0.006 x 0.12^2 ) ] wf
wf = 0.11 rad/s
e) Before collision,
KEi = m v^2 /2 = 0.006 x (1 x 10^3)^2 / 2 = 3000 J
after collision,
KEf = I wf^2 /2 = [ (19.7 x 1^2 /3) + (0.006 x 0.12^2 ) ](0.11^2) / 2
= 0.04 J
hence KE energy is less than as it intially was.
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