Answered

IDNLearn.com connects you with a community of experts ready to answer your questions. Join our interactive Q&A platform to receive prompt and accurate responses from experienced professionals in various fields.

A bullet is fired horizontally into an initially stationary block of wood suspended by a string and remains embedded in the block. The bullet’s mass is m = 0.0075 kg, while that of the block is M = 0.95 kg. After the collision the block/bullet system swings and reaches a maximum height of h = 1.1 m above its initial height. Neglect air resistance.

Calculate the ratio, expressed as a percent, of the kinetic energy of the block/bullet system immediately after the collision to the initial kinetic energy of the bullet.

KEf/KEi(%) =

Sagot :

Onyebuchinnajiidn

The ratio of the kinetic energy of the block/bullet system immediately after the collision to the initial kinetic energy of the bullet is 0.78 %.

Final velocity of the block/bullet system

Apply the principle of conservation of energy to determine the final velocity of the block/bullet system.

K.E = P.E

¹/₂mv² = mgh

¹/₂v² = gh

v² = 2gh

v = √2gh

where;

  • h is the maximum height reached by the system
  • v is the initial velocity of the system

v = √(2 x 9.8 x 1.1)

v = 4.64 m/s

Initial velocity of the bullet

Apply the principle of conservation of linear momentum.

m₁u₁ + m₂u₂ = v(m₁ + m₂)

where;

  • u₁ is the initial velocity of the bullet
  • u₂ is the initial velocity of the block
  • v is the final velocity after collision
  • m₁ is mass bullet
  • m₂ is mass of block

(0.0075)u₁ + (0.95)(0) = 4.64(0.0075 + 0.95)

0.0075u₁ = 4.4428

u₁ = 4.4428/0.0075

u₁ = 592.37 m/s

Initial kinetic energy of the bullet

K.Ei = ¹/₂m₁u₁²

K.Ei = ¹/₂(0.0075)(592.37)²

K.Ei = 1,315.88 J

Final kinetic energy of the block/bullet system

K.Ef = ¹/₂(m₁ + m₂)v²

K.Ef = ¹/₂(0.0075 + 0.95)(4.64)²

K.Ef = 10.31 J

Ratio of final kinetic energy to initial kinetic energy

= K.Ef/K.Ei x 100%

= (10.31 / 1,315.88) x 100%

= 0.78 %

Learn more about kinetic energy here: https://brainly.com/question/25959744

#SPJ1

Thank you for using this platform to share and learn. Keep asking and answering. We appreciate every contribution you make. IDNLearn.com is committed to providing accurate answers. Thanks for stopping by, and see you next time for more solutions.