(3) This problem deals with a method for measuring the muzzle velocity of a rifle. A rifle with unknown muzzle velocity vo fires a bullet with mass m into a large block of wood with mass M that is sitting on a horizontal surface. The velocity of the block right after the (inelastic) collision is v. The block then slides a distance d along the surface and comes to a stop. The coefficient of kinetic friction between the block of wood and the surface is μlk. (a) Use conservation of momentum (during the collision) and the work-energy theorem (after the collision) to show that the muzzle velocity of the rifle is given by: , = (m² + M) √√2 μgd m (b) Calculate the muzzle velocity of the rifle if m= 5.00 g, M = 1.20 kg, d = 14.6 cm, and μ = 0.56. [answer: vo= 305 m/s]

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Chapter6: Momentum, Impulse, And Collisions
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(3) This problem deals with a method for measuring the muzzle velocity of a rifle. A rifle with unknown
muzzle velocity vo fires a bullet with mass m into a large block of wood with mass M that is sitting on a
horizontal surface. The velocity of the block right after the (inelastic) collision is v. The block then slides
a distance d along the surface and comes to a stop. The coefficient of kinetic friction between the block of
wood and the surface is μk.
(a) Use conservation of momentum (during the collision) and the work-energy theorem (after the collision)
to show that the muzzle velocity of the rifle is given by:
20
=
(m + M) √2 µx8d
m
(b) Calculate the muzzle velocity of the rifle if m= 5.00 g. M = 1.20 kg. d = 14.6 cm, and µ = 0.56.
[answer: vo = 305 m/s]
Transcribed Image Text:(3) This problem deals with a method for measuring the muzzle velocity of a rifle. A rifle with unknown muzzle velocity vo fires a bullet with mass m into a large block of wood with mass M that is sitting on a horizontal surface. The velocity of the block right after the (inelastic) collision is v. The block then slides a distance d along the surface and comes to a stop. The coefficient of kinetic friction between the block of wood and the surface is μk. (a) Use conservation of momentum (during the collision) and the work-energy theorem (after the collision) to show that the muzzle velocity of the rifle is given by: 20 = (m + M) √2 µx8d m (b) Calculate the muzzle velocity of the rifle if m= 5.00 g. M = 1.20 kg. d = 14.6 cm, and µ = 0.56. [answer: vo = 305 m/s]
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