(a) Before it hits the door, does the bullet have angular momentum relative the
ID: 1477720 • Letter: #
Question
(a) Before it hits the door, does the bullet have angular momentum relative the door's axis of rotation?
yesno
Explain your answer.
(b) Is mechanical energy conserved in this collision? Answer without doing a calculation.
yesno
(c) At what angular speed does the door swing open immediately after the collision? (The door has the same moment of inertia as a rod with axis at one end.)
rad/s
(d) Calculate the energy of the door-bullet system and determine whether it is less than or equal to the kinetic energy of the bullet before the collision. (Give the kinetic energy of the door-bullet system just after collision.)
J
Explanation / Answer
a) angular momentum is given by
L=m*(cross product of r and V)
where r is distance vector and V is veloicty vector
as here angle is not 0, angular momentum will exist
so answer is yes.
part b:
mechanical energy is not conserved as the collision is not elastic in nature and energy will be lost in heat energy as
bullet is embedded into the door.
part c:
linear momentum is conserved.
hence initial linear momentum=final linear momentum
==>mass of bullet*speed of bullet=(mass of bullet+mass of door)*speed of combined system
==>speed of combined system=0.005*1000/(0.005+15.3)=0.3267 m/s
radius of rotation just when the bullet strikes=1-0.086=0.914 m
hence angular speed=linear speed/radius=0.3574 rad/sec
part d:
kinetic energy of the bullet before collision=0.5*mass of bullet*speed of bullet^2
=0.5*0.005*10^6=2500 J
moment of inertia of the door about the hinge=moment of inertia of a rod about an axis passing through one of its edges
=(1/3)*mass*length^2
=(1/3)*15.3*1^2=5.1 kg.m^2
moment of inertia of the embedded bullet=mass*distance from the axis^2
=0.005*0.914^2=4.17698*10^(-4) kg.m^2
total moment of inertia=5.1+4.17698*10^(-4)=5.10417698 kg.m^2
final kinetic energy of bullet+door system=0.5*total moment of inertia*angular speed^2
=0.3259 J
hence it is significantly lesser than the initial energy of the bullet.
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