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Springs (4 Multiple choice)

  1. Oct 25, 2013 #1
    1. Two blocks of equal mass are each pushed (from rest) along a frictionless surface a distance d. The force applied to block B is four times that applied to block A. What is the velocity of block B, relative to that of block A, vA?

    a) 4 vA
    b) 2 vA
    c) vA
    d) vA/2
    e) vA/4

    2. What is the kinetic energy of block B relative to that of block A, KA?

    a) 4 KA
    b) 2 KA
    c) KA
    d) KA/2
    e) KA/4

    3. The same work is done compressing spring A or spring B from their equilibrium lengths. The spring constant of spring A is four times that of spring B. How much is spring B compressed relative to spring A, xA?

    a) 8 xA
    b) 4 xA
    c) 2 xA
    d) xA/2
    e) xA/4
    f) xA/8

    4. What is the maximum force applied to spring B relative to that applied to spring A, FA?

    a) 8 FA
    b) 4 FA
    c) 2 FA
    d) FA/2
    e) FA/4
    f) FA/8

    For 1. I figure that pushing B with 4 times the force would make it accelerate 4 times as fast, thus making the final velocity 4 times as fast as the velocity of block A if they both start at rest. So I chose a)

    For 2. I figure that since the velocity of B is 4 times larger than the velocity of A, then the KE = 1/2 m*v2 would make the KE of B 4 times larger than the KE of A, so I chose a) again.

    For 3. I figure that kA is 4kB. If the work for both is equal, then F*dA = F*dB, and since kA = 4kB, then B is compressed 4 times as much, so I chose b). I am unsure about this one.

    For 4. I'm kind of confused...

    Any help at all would be appreciated!
  2. jcsd
  3. Oct 25, 2013 #2
    First consider Q.1) .Your answer and reasoning both are incorrect .Do you know Work Kinetic Energy Theorem ?

    It states Wnet = ΔKE i.e net work done by all the external forces is equal to the change in the kinetic energy of the body .

    Just Apply it .What do you get ?
  4. Oct 25, 2013 #3
    You should not go on your logic. Write equations of motion and then you should understand how many problems are wrong!!!(first is wrong and i think others too are wrong.)
  5. Oct 25, 2013 #4
    So in 1. for B, it's 1/2 mv2 = 4*F*d?
  6. Oct 25, 2013 #5
    Yes..that is right .
  7. Oct 25, 2013 #6
    So I work that out for B and get v2 = (8*F*d)/m.

    I work it out for A and get v2 = (2*F*d)/m

    So is vB not 4 times larger than vA?
  8. Oct 25, 2013 #7
    you should take squareroots on both sides
  9. Oct 25, 2013 #8
    No...This means vB2 is equal to four times vA2 :smile:
  10. Oct 25, 2013 #9
    Oh damn. So vB = 2*vA?
  11. Oct 25, 2013 #10
  12. Oct 25, 2013 #11
    that's right:smile:
    So what is the correct option of 1
  13. Oct 25, 2013 #12
    So 1. is b)!

    Now onto the next ones...
  14. Oct 25, 2013 #13
    No,thats wrong.
    see what is asked "What is the velocity of block B, relative to that of block A"
  15. Oct 25, 2013 #14

    So what is the answer according to you ?
  16. Oct 25, 2013 #15
    I am utterly confused
  17. Oct 25, 2013 #16
    No need to get confused ..Just carry on with the next part..

    Let nil1996 answer my question .
  18. Oct 25, 2013 #17
    block B is moving at a velocity 2Va and block A is moving at speed Va
    So the relative velocity is Va . isn't it right??
  19. Oct 25, 2013 #18
    That is simply wrong understanding.

    Please read question carefully...Here relative means in comparision to .The question doesn't ask about relative velocity .
  20. Oct 25, 2013 #19
    If i say you are moving at 4 m/s and i at 2m/s in same direction and ask "what is your velocity relative to me?"
    The answer would be 2m/s.

    I think the problems is similar too.
  21. Oct 25, 2013 #20
    Where is it mentioned that the two blocks are moving in the same direction ?

    The question is asking for the relation between the two velocities ,not relative velocity.
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