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A simple question about Force

  1. Jan 18, 2017 #1
    1. The problem statement, all variables and given/known data
    The Zacchini family was renowned for their human-cannonball act in which a family member was shot from a cannon using either elastic bands or compressed air.In one version of the act,Emanuel Zacchini was shot over three Ferris wheels to land in a net at same height as the open end of the cannon and at a range of 69 m.He was propelled inside the barrel for 5.2 m and launched at an angle of 530 ( degree).If his mass was 85 kg and he underwent cosntant acceleration inside the barrel,what was the magnitude of the force propelling him ? ( Hint:Treat the launch as though it were along aa ramp at 530 ( degree).Neglect air drag )

    2. Relevant equations
    [tex]\vec F_t=m \vec a [/tex] [tex]m=mass[/tex] [tex]\vec F_t =Total \ Force[/tex]
    [tex]\vec w_=m \vec g [/tex] [tex]g=9.8 m/s^2[/tex]
    [tex] v-v_0=at[/tex] [tex]v_0=inital \ velocity[/tex]

    Projectile motion equations (In this question they will be in different forms I guess and I dont know how to find them thats my problem)



    3. The attempt at a solution

    I upload a picture.After that solution I am stucked.Cause theres acceleration and also velocity of the object and I have to apply them to projectile motion equations.

    Here my try
    For x axis ;

    [tex]69m=v_0cos(53^0) t+\frac 1 2 acos(53^0)t^2 [/tex]
    Simply I couldnt solve.

    For y axis;
    Here things are more complicated
    Simply I couldnt solve.

    Also another referance frame would be easier to solve but I couldnt put the forces in there something's doesnt make sense.I would be happy If somebody help me
    Thanks
     

    Attached Files:

  2. jcsd
  3. Jan 18, 2017 #2

    phinds

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    Just FYI, your image is ridiculously small and completely unreadable.
     
  4. Jan 18, 2017 #3
    Then this is the best thing I can do

    Here F is The force that cannonball applies, I showed my referance frame, m is mass of object, a is the acceleration of object inside the cannonball.
     

    Attached Files:

  5. Jan 18, 2017 #4
    In this referance frame I can write the components of force.But is it a better then my pre-referance frame...
    Components are ;
    w=mg (-y)
    N=Ncos37 (x) + Nsin37(y)
    F=Fcos53 (-x) + Fsin53(y)

    so Ftotal=ma cos53 (-x) + ma sin53 (y)

    so ;
    -ma cos53=Ncos37-Fcos53
    and
    ma sin53 =-mg+Nsin37+Fsin53
     

    Attached Files:

  6. Jan 18, 2017 #5

    haruspex

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    Deal with the trajectory first. Find the KE with which he must emerge from the barrel.
     
  7. Jan 19, 2017 #6
    I can use only Newtons's Law.
    And I just dont wanna solve the question and leave there.I want to know where am I doing wrong.
    Thanks
     
  8. Jan 19, 2017 #7

    haruspex

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    You will have to deal with the trajectory at some point, and that also uses Newton's laws.
    But if you wish to start with the cannon, ok.
    It will be much easier if you use a coordinate parallel to the ramp. Try writing the F=ma equation for that.
    You won't need to work with a second coordinate.
     
  9. Jan 19, 2017 #8
    I didnt want to use energy cause the book hasnt arrived there yet.So this question has a solution without using any energy transformation.(If that was your point)
    So theres two equations.(Theres a pic in my #3 post A simple question about Force )
    ##-ma = - F + mgsin(53^0) ## (Eq-1)
    ##F:\text{The force that we wanted to know}##
    ##a:\text{acceleration of object}##
    ##N=mgcos(53^0)## (Eq-2)
     
  10. Jan 19, 2017 #9

    haruspex

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    Ok, that relates F to a. Next, you need to relate a to the launch speed. What equations do you know that would do that?
     
  11. Jan 20, 2017 #10
    ##v^2-(v_0)^2=2a(x-x_0)## So here ##v_0=0## and ##x_0=0##
    so If we use this equation to in our referance frame we willl get

    ##v^2-0=2(-a)((-x)-0)## which equals to;
    ## v^2=2ax##
     
  12. Jan 20, 2017 #11
    Ok I solved the problem.Just I made a simple false assumption.And then I couldnt solve cause of that.Now I solved thanks again
     
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