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Question on mechanics?

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  • 16-07-2009 7:43pm
    #1
    Tones66
    Registered Users Posts: 49 ✭


    Hi. I couldn't do this question. If anyone fancies themselves could you post your solution.Any help will be appreciated. I'm stuck. Thanks.

    An unplanned impact has occurred between vehicle A and a stationary vehicle B. Markings on the road indicate that after the impact B slid a distance of 2m before coming to rest. The coefficient of kinetic friction between B's tyres and the road is 0.7 and laboratory tests indicate that a coefficient of restitution e=0.4 is appropriate for this type of impact. Mass vehicle A = 1100kg. Mass vehicle B = 1300kg.

    (a) Assuming that only single impact occurred, determine whether vehicle A was exceeding the relevant speed limit of 30 km/h before the impact.(15 marks)

    (b) Determine the change in momentum for vehicle B. I the duration of the impact is estimated to be 0.01 s,estimate the average force exerted on B by A during impact.(5 marks)

    (c)Determine the percentage of mechanical energy lost in the impact and briefly discuss possible explanations for the energy loss.(5 marks)


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    #2
    HIB
    Registered Users Posts: 259 ✭✭HIB


    Tones66 wrote: »
    Hi. I couldn't do this question. If anyone fancies themselves could you post your solution.Any help will be appreciated. I'm stuck. Thanks.

    An unplanned impact has occurred between vehicle A and a stationary vehicle B. Markings on the road indicate that after the impact B slid a distance of 2m before coming to rest. The coefficient of kinetic friction between B's tyres and the road is 0.7 and laboratory tests indicate that a coefficient of restitution e=0.4 is appropriate for this type of impact. Mass vehicle A = 1100kg. Mass vehicle B = 1300kg.

    (a) Assuming that only single impact occurred, determine whether vehicle A was exceeding the relevant speed limit of 30 km/h before the impact.(15 marks)

    (b) Determine the change in momentum for vehicle B. I the duration of the impact is estimated to be 0.01 s,estimate the average force exerted on B by A during impact.(5 marks)

    (c)Determine the percentage of mechanical energy lost in the impact and briefly discuss possible explanations for the energy loss.(5 marks)


    I had a full explanaiton written out and then got logged off, so sorry for the shortness of this answer!

    You have two equations to work with. Conservation of momentum and the definition of coefficient of restitution
    Primed = after collision
    Unprimed = before the collision

    mava + mbvb = mava' + mbvb'
    vb'-va' = E(va - vb)

    There are 3 unknowns (vb=0)

    You can find vb' from the friction information. Use v = u + 2as
    u in this equation is vb' in the above equations. You know s and v= 0
    (car is decelerating due to friction and eventually stops)

    Find a, the acceleration (negative) from F = uN = uW = umg = ma
    i.e. a = ug (u=coeff of dynamic friction)

    You can then find u(vb'). Then, going back to the initial eqns, you have 2 eqns in two unknowns and can solve for all velocities.

    For part B, you just need to know that momentum = mass x velocity

    Also, acceleration = (change in velocity)/time taken = vb'-vb/0.01
    Then F= ma = mb * (vb'-vb)/0.01

    For part C you just need to calculate the change to the kinetic energy


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    #3
    Tones66
    Registered Users Posts: 49 ✭Tones66


    HIB wrote: »
    I had a full explanaiton written out and then got logged off, so sorry for the shortness of this answer!

    You have two equations to work with. Conservation of momentum and the definition of coefficient of restitution
    Primed = after collision
    Unprimed = before the collision

    mava + mbvb = mava' + mbvb'
    vb'-va' = E(va - vb)

    There are 3 unknowns (vb=0)

    You can find vb' from the friction information. Use v = u + 2as
    u in this equation is vb' in the above equations. You know s and v= 0
    (car is decelerating due to friction and eventually stops)

    Find a, the acceleration (negative) from F = uN = uW = umg = ma
    i.e. a = ug (u=coeff of dynamic friction)

    You can then find u(vb'). Then, going back to the initial eqns, you have 2 eqns in two unknowns and can solve for all velocities.

    For part B, you just need to know that momentum = mass x velocity

    Also, acceleration = (change in velocity)/time taken = vb'-vb/0.01
    Then F= ma = mb * (vb'-vb)/0.01

    For part C you just need to calculate the change to the kinetic energy


    Hey thanks very much. That looks good....A very good first post by any standards :D


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