College physics

posted by .

A 0.006 00-kg bullet traveling horizontally with a speed of 1.00 x 10^3 m/s enters an 20.1-kg door, imbedding itself 10.9 cm from the side opposite the hinges as in the figure below. The 1.00-m wide door is free to swing on its frictionless hinges.


At what angular speed does the door swing open immediately after the collision?

Calculate the energy of the bullet-door system and determine whether it is less than or equal to the kinetic energy of the bullet before the collision (what is the final and initial KE's)

  • College physics -

    I'll assume that 1.00 103 means 1x10^3

    a)
    Yes. Any object which has a velocity vector which does not pass directly through the chosen axis has angular momentum about that axis.


    b)
    No, mechanical energy is not conserved. Angular momentum is conserved, and any excess energy is dissipated within the door.


    c)
    W.before = W.after
    Solve for both, then solve for final w. (note that W is angular momentum, w is angular velocity)

    W.before = I.bullet * w.bullet + I.door * w.door
    I.bullet = m.bullet * (.91 m)^2
    w.bullet = V.bullet / (.91 m)
    W.before = m.bullet * V.bullet * (.91 m) + 0

    W.after = I.bullet * w.bullet + I.door + w.door
    W.after = m.bullet * (.91 m)^2 * w.bullet + 1/3 * m.door * (1m)^2 * w.door
    since w.bullet = w.door, we'll just call that w

    W.after = w * (m.bullet * (.91 m)^2 + 1/3 * m.door * (1m)^2)

    Set W.before = W.after and solve for w

    m.bullet * V.bullet * (.91 m) + 0 = w * (m.bullet * (.91 m)^2 + 1/3 * m.door * (1m)^2)
    .006 kg * 1000 m/s * .91 m = w * (.006 kg * (.91 m)^2 + 1/3 * 18.2 kg * (1 m)^2)
    5.46 kgm^2/s = w * 6.0716 kgm^2

    w = .8992 radians/second



    d)
    Before:
    Ek = 1/2 * m.bullet * V.bullet^2
    Ek = 1/2 * .006 kg * 1000000 m^2/s^2
    Ek = 3000 joules

    After:
    Ek = I.bullet * w^2 + I.door * w^2
    Ek = (.8992 rad/sec)^2 * (.006 kg * (.91 m)^2 + 1/3 * 18.2 kg * (1m)^2)
    Ek = 4.909 joules

    Note that kinetic energy after is significantly less than kinetic energy before.

Respond to this Question

First Name
School Subject
Your Answer

Similar Questions

  1. Physics

    A 0.006-kg bullet traveling horizontally with a speed of 1.00 103 m/s enters an 21.1-kg door, imbedding itself 10.4 cm from the side opposite the hinges as in the figure below. The 1.00-m-wide door is free to swing on its hinges. (c) …
  2. physics

    A 0.005-kg bullet traveling horizontally with a speed of 1.00 103 m/s enters an 20.3-kg door, imbedding itself 10.6 cm from the side opposite the hinges as in the figure below. The 1.00-m-wide door is free to swing on its hinges. (c) …
  3. physiC

    A uniform door (0.81 m wide and 2.1 m high) weighs 150 N and is hung on two hinges that fasten the long left side of the door to a vertical wall. The hinges are 1.9 m apart. Assume that the lower hinge bears all the weight of the door. …
  4. Physics

    A uniform 22 kg door that is 2.5 m high by 0.80 m wide is hung from two hinges that are 20 cm from the top and 20 cm from the bottom. If each hinge supports half the weight of the door, find the magnitude and direction of the horizontal …
  5. Physics: Rotational Motion

    A 0.005kg bullet travelling horizontally with a speed of 1000m/s enters an 18kg door, embedding itself 10cm from the side opposite the hinges as in figure. The 1m wide door is free to swing on the hinges. a) Before it hits the door, …
  6. Physics

    There is a door that is 1.0 m wide and can rotate about a vertical axis without friction. The door’s mass is 15 kg and is free to swing open. Someone fires a 10 g bullet at 400 m/s into the exact center of the door, perpendicular …
  7. Physics

    A 15 kg, 1m wide door which has frictionless hinges is closed but unlocked. A 400 g ball hits the exact middle of the door at a velocity of 35 m/s and bounces off elastically, thereby causing the door to slowly swing open. How long …
  8. Physics

    A 15 kg, 1m wide door which has frictionless hinges is closed but unlocked. A 400 g ball hits the exact middle of the door at a velocity of 35 m/s and bounces off elastically, thereby causing the door to slowly swing open. How long …
  9. Physics

    A 10 g dart traveling at 400 m/s sticks into a 10 kg, 1 m wide door at the edge opposite the hinge causing the door to swing open. What is the angular velocity of the door immediately after impact?
  10. Physics

    A 10 g dart traveling at 400 m/s sticks into a 10 kg, 1 m wide door at the edge opposite the hinge causing the door to swing open. What is the angular velocity of the door immediately after impact?

More Similar Questions