A wooden block of mass M resting on a frictionless, horizontal surface is attach

Question

A wooden block of mass M resting on a frictionless, horizontal surface is attached to a rigid rod of length and of negligible mass. The rod is pivoted at the other end. A bullet of mass m traveling parallel to the horizontal surface and perpendicular to the rod with speed v hits the block and becomes embedded in it.

(a) What is the angular momentum of the bullet–block system about a vertical axis through the pivot? (Use any variable or symbol stated above as necessary.)
L =

(b) What fraction of the original kinetic energy of the bullet is converted into internal energy in the system during the collision? (Use any variable or symbol stated above as necessary.)

=

Explanation / Answer

(a)

the angular momentum of the bullet–block system about a vertical axis through the pivot

L = mvL

(b)

from the conservation of angular momentum

L = Iw

here I = ML2/3 + mL2 = (M/3 +m)L2

initial kinetic energy is

KE1 = mv^2/2

final kinetic energy KE2 = I w^2/2

the internal energy is

  E- E' = KE1- KE2

the fraction of the original kinetic energy of the bullet is converted into internal energy in the system during the collision

=KE1- KE2/ E

= E- E'/ E

=1 - I2/mv2

=1 - (I/mv)2*(m/I)

= 1 - mL2/l

= 1 - m/(M/3 + m)

= M/(M + 3m)

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.