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1 October, 11:29

A luge and its rider, with a total mass of 85 kg, emerge from a downhill track onto a horizontal straight track with an initial speed of 37 m/s. If a force slows them to a stop at a constant rate of 2.0 m/s2, (a) what magnitude F is required for the force, (b) what distance d do they travel while slowing, and (c) what work W is done on them by the force

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  1. 1 October, 12:13
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    a) 170N b) 342.25m c) 58.2KJ

    Explanation:

    a) magnitude F required for the force can be gotten using the Newton's second law of motion.

    Force = mass * acceleration

    Given mass = 85kg

    acceleration = 2.0m/s²

    Force = 85*2

    Force = 170N

    Magnitude of force required is therefore 170N

    b) To get the distance d at which they travel, we will use the equation of motion;

    v² = u²+2ad where

    v is the final velocity = 0m/s

    u is the initial velocity = 37m/s

    a is the acceleration = - 2m/s² (since the body is slowing down while travelling)

    d is the distance travelled while slowing

    Substituting the values given into the formula we will have;

    0² = 37²-2 (2) d

    -37² = - 4d

    d = 342.25m

    c) Work done on them by the force can be calculated using the formula;

    Work done = Force * Distance

    Work done = 170*342.25

    Work done = 58,182.5Joules

    = 58.2KJ
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