You have been asked to design a 'ballistic spring system' to measure the speed of bullets. So a bullet of mass m is fired horizontally into a block of mass M. The block, with the embedded bullet, then slides across a frictionless horizontal table and collides with a horizontal spring, whose spring constant is k, and the opposite end of the spring is anchored to a wall. Subsequently, the spring is measured to have a maximum compression d. (1) Derive an expression for the bullet's initial speed v3 in terms of m, M, k and d. (11) What was the speed of a 5.0 g bullet if the block's mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 10 cm? (iii) What fraction of the bullet's initial kinetic energy is "lost"? (Give 4 decimal places to this calculation.) Where did it go to?
You have been asked to design a 'ballistic spring system' to measure the speed of bullets. So a bullet of mass m is fired horizontally into a block of mass M. The block, with the embedded bullet, then slides across a frictionless horizontal table and collides with a horizontal spring, whose spring constant is k, and the opposite end of the spring is anchored to a wall. Subsequently, the spring is measured to have a maximum compression d. (1) Derive an expression for the bullet's initial speed v3 in terms of m, M, k and d. (11) What was the speed of a 5.0 g bullet if the block's mass is 2.0 kg and if the spring, with k = 50 N/m, was compressed by 10 cm? (iii) What fraction of the bullet's initial kinetic energy is "lost"? (Give 4 decimal places to this calculation.) Where did it go to?
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Transcribed Image Text:You have been asked to design a 'ballistic spring system' to measure the speed
of bullets. So a bullet of mass m is fired horizontally into a block of mass M. The
block, with the embedded bullet, then slides across a frictionless horizontal table
and collides with a horizontal spring, whose spring constant is k, and the
opposite end of the spring is anchored to a wall. Subsequently, the spring is
measured to have a maximum compression d.
(i)
Derive an expression for the bullet's initial speed v in terms of m, M, k
and d.
(ii)
What was the speed of a 5.0 g bullet if the block's mass is 2.0 kg and if
the spring, with k = 50 N/m, was compressed by 10 cm?
(ii)
What fraction of the bullet's initial kinetic energy is "lost"?
(Give 4 decimal places to this calculation.)
Where did it go to?
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