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10 February, 12:52

Suppose a child drives a bumper car head on into the side rail, which exerts a force of 3400 N on the car for 0.400 s. (a) What impulse (in kg · m/s) is imparted by this force? (b) Find the final velocity (in m/s) of the bumper car if its initial velocity was 3.20 m/s and the car plus driver have a mass of 200 kg. You may neglect friction between the car and floor.

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  1. 10 February, 13:13
    0
    a) 1360kgm/s b) 5.14m/s

    Explanation:

    a) According to Newton's second law of motion,

    Force = mass * acceleration

    F = ma

    since acceleration = change in velocity (v-u) / time (t)

    F = m (v-u) / t

    Ft = m (v-u) = Impulse.

    Impulse is defined as change in momentum of a body. It can be expressed as;

    Impulse = Ft = m (v-u)

    Given force exerted on the car = 3400N

    time taken = 0.400seconds

    Impulse = 3400*0.4

    Impulse = 1360kgm/s

    b) To find the final velocity / (v) of the car, we will use the equation of motion below;

    v = u+at where;

    v is the final velocity = ?

    u is the initial velocity = 3.2m/s

    a is the acceleration

    t is the time taken = 0.4second

    To get the acceleration, we will use the formula F = ma where;

    m is the mass

    F is the force

    a is the acceleration

    a = F/m = 3400/200

    a = 17m/s²

    Substituting the values to get the final velocity 'v' we have;

    v² = 3.2²+17 (0.4)

    v² = 10.24+6.8

    v² = 17.04

    v = √17.04

    v = 4.13m/s

    The final velocity of the bumper car is 4.14m/s
  2. 10 February, 13:22
    0
    (a) 1360 Ns

    (b) 10 m/s

    Explanation:

    (a)

    Impulse: This can be defined as the product of force and time. The S. I unit of impulse is Ns

    From Newton's third law,

    The expression for impulse is given as,

    I = F*t ... Equation 1

    Where I = Impulse, F = Force, t = Time.

    Given: F = 3400 N, t = 0.4 s

    Substitute into equation 1

    I = 3400*0.4

    I = 1360 Ns

    (b)

    From newton third law of motion,

    Impulse = Change in momentum.

    I = m (v-u) ... Equation 2

    Where I = impulse, m = mass of the car plus the driver, v = final velocity of the bumper car, u = initial velocity of the car.

    make v the subject of the equation

    v = (I/m) + u ... Equation 3

    Given: I = 1360 Ns, m = 200 kg, u = 3.2 m/s

    Substitute into equation 3

    v = (1360/200) + 3.2

    v = 6.8+3.2

    v = 10 m/s
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