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A body of mass 100 g moving at 10 m/s collides and rebounds with a speed of 2 m/s. Calculate the change in momentum.

Physics

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Answer

1.2 kg m/s\text{1.2 kg m/s}

Step-by-step solution

5 steps
  1. Convert the mass to kilograms.

    Given mass m=100 gm = 100 \text{ g}.

    m=100 g×1 kg1000 g=0.1 kgm = 100 \text{ g} \times \frac{1 \text{ kg}}{1000 \text{ g}} = 0.1 \text{ kg}
  2. Define the initial and final velocities, considering direction.

    Let the initial direction of motion be positive.
    Initial velocity vi=10 m/sv_i = 10 \text{ m/s}.
    After collision, the body moves in the opposite direction, so the final velocity is negative.
    Final velocity vf=−2 m/sv_f = -2 \text{ m/s}.

  3. Calculate the initial momentum (pip_i).

    Momentum is given by p=mvp = mv.

    pi=mvip_i = m v_i pi=0.1 kg×10 m/sp_i = 0.1 \text{ kg} \times 10 \text{ m/s} pi=1.0 kg m/sp_i = 1.0 \text{ kg m/s}
  4. Calculate the final momentum (pfp_f).

    pf=mvfp_f = m v_f pf=0.1 kg×(−2 m/s)p_f = 0.1 \text{ kg} \times (-2 \text{ m/s}) pf=−0.2 kg m/sp_f = -0.2 \text{ kg m/s}
  5. Calculate the change in momentum (Δp\Delta p).

    The change in momentum is the final momentum minus the initial momentum.

    Δp=pf−pi\Delta p = p_f - p_i Δp=−0.2 kg m/s−1.0 kg m/s\Delta p = -0.2 \text{ kg m/s} - 1.0 \text{ kg m/s} Δp=−1.2 kg m/s\Delta p = -1.2 \text{ kg m/s}

    The magnitude of the change in momentum is 1.2 kg m/s1.2 \text{ kg m/s}. The negative sign indicates the change is in the direction opposite to the initial motion.

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