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Math Help - momentum

  1. #1
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    momentum

    The handbrake of a stationary vehicle of mass 1.5 Tonnes fails while it is parked on a 250 slope. It rolls 20m down the slope before colliding with, and locking on to, another parked vehicle of mass 0.9 Tonnes.
    a) Estimate the velocity of the two vehicles immediately after the impact.

    b) Will the vehicles come to a halt at some time after the collision, or continue down the hill? Assume a coefficient of friction between the tyres and the road of
    μk=0.8, and that the handbrake only operates on the rear wheels of the vehicle.

    could someone please explain how to solve this problem? cheers x

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  2. #2
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    Momentum (and energy)

    Hi -

    You'll have to make various assumptions here, maybe something like:

    • The handbrake of the first vehicle fails completely, and that there is no resistance to this vehicle rolling down the hill. In this case, you can use energy to work out its speed before impact.
    • Then use conservation of momentum to find the speed of the locked vehicles immediately after the impact.
    • You then have to make a further assumption about the weight distribution of the second vehicle. If its weight is evenly distributed between its (two?) axles, then the contact forces between the road and the front and rear wheels will be the same - but of course, there will only be a friction force on the rear wheels. This will give you an estimate of the total friction force exerted on the two locked vehicles. You can then use force = mass x acceleration to find what happens next.

    Is that enough detail to get you started?

    Grandad
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