(2) A block with mass m is sliding with speed vo on a surface that is so slippery it can be considered to befrictionless. The sliding block collides with a second stationary block with mass 4m. Both blocks sticktogether and continue sliding with speed v. Take both blocks to be the "system" and assume that no netexternal force acts on it so the momentum of the system is conserved (constant).(a) What is vin terms of vo? (Hint: Use conservation of momentum.) [answer: v=v0/5](b) What is the initial kinetic energy of the system (K) in terms of m and vo? [answer: Ki = ¹/2mv0²](c) What is the final kinetic energy of the system (K) expressed as a fraction of Ki? [answer: K₂= K₂](d) What is the change in kinetic energy of the system (AK) expressed as a fraction of Ki?[answer: AK = - K;](e) By what factor does the kinetic energy of the system change during the collision? That is, what is theratio Kf / K₁? [answer: = 1, or Kf = K./5, i.e., the kinetic energy decreases by a factor of 5.]Ki(f) What percentage of Ki is lost to heat/sound energy during the collision? [answer: 80%](g) How much heat/sound energy (Q) is produced during the collision, expressed as a fraction of Ki?[answer: Q = K₂]

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(2) A block with mass m is sliding with speed vo on a surface that is so slippery it can be considered to be frictionless. The sliding block collides with a second stationary block with mass 4m. Both blocks stick together and continue sliding with speed v. Take both blocks to be the "system" and assume that no net external force acts on it so the momentum of the system is conserved (constant). (a) What is vin terms of vo? (Hint: Use conservation of momentum.) [answer: v=v0/5] (b) What is the initial kinetic energy of the system (K) in terms of m and vo? [answer: K₁=½/2 mv0²] (c) What is the final kinetic energy of the system (K) expressed as a fraction of Ki? [answer: K; = - K;] (d) What is the change in kinetic energy of the system (AK) expressed as a fraction of Ki? [answer: AK = -K;) (e) By what factor does the kinetic energy of the system change during the collision? That is, what is the ratio K+/ K₁? [answer: K=1, or Kf=K₁/5, i.e., the kinetic energy decreases by a factor of 5.]

(2) A block with mass m is sliding with speed vo on a surface that is so slippery it can be considered to be frictionless. The sliding block collides with a second stationary block with mass 4m. Both blocks stick together and continue sliding with speed v. Take both blocks to be the "system" and assume that no net external force acts on it so the momentum of the system is conserved (constant). (a) What is vin terms of vo? (Hint: Use conservation of momentum.) [answer: v=v0/5] (b) What is the initial kinetic energy of the system (K) in terms of m and vo? [answer: K₁=½/2 mv0²] (c) What is the final kinetic energy of the system (K) expressed as a fraction of Ki? [answer: K; = - K;] (d) What is the change in kinetic energy of the system (AK) expressed as a fraction of Ki? [answer: AK = -K;) (e) By what factor does the kinetic energy of the system change during the collision? That is, what is the ratio K+/ K₁? [answer: K=1, or Kf=K₁/5, i.e., the kinetic energy decreases by a factor of 5.]

Classical Dynamics of Particles and Systems

5th Edition

ISBN:9780534408961

Author:Stephen T. Thornton, Jerry B. Marion

Publisher:Stephen T. Thornton, Jerry B. Marion

Chapter9: Dynamics Of A System Of Particles

Section: Chapter Questions

Problem 9.36P: In an elastic collision of two particles with masses m1 and m2, the initial velocities are u1 and u2...

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